{"id":1209,"date":"2023-08-15T20:09:08","date_gmt":"2023-08-15T14:39:08","guid":{"rendered":"https:\/\/iitmadrasstudentscommunity.me\/?p=1209"},"modified":"2023-08-15T20:11:29","modified_gmt":"2023-08-15T14:41:29","slug":"statistics-week-11-graded-assignments-iit-madras","status":"publish","type":"post","link":"https:\/\/iitmadrasstudentscommunity.me\/statistics-week-11-graded-assignments-iit-madras\/","title":{"rendered":"Statistics Week 11 Graded Assignments IIT Madras"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"1209\" class=\"elementor elementor-1209\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b3e3c44 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b3e3c44\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-905de55\" data-id=\"905de55\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c221419 elementor-widget elementor-widget-text-editor\" data-id=\"c221419\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p><em style=\"font-family: &quot;Trebuchet MS&quot;, sans-serif;\">Statistics week 11 graded assignment Complete&nbsp; Solutions Are Discussed In This Blog We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons Not Able To Complete Graded Assignments&nbsp;<\/em><br><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a943dfe elementor-widget elementor-widget-text-editor\" data-id=\"a943dfe\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div id=\"7OChO7L3MK7O\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div id=\"7OChO7L3MK7O.0.4809265847992320\" class=\"qt-mc-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">A match predictor claims that he can predict the result of a match correctly 77% of the time. It is agreed that his claim will be accepted if he correctly predicts the results of at least 4 of 8 matches. What is the probability that his claim gets rejected?<\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"7OChO7L3MK7O.0.4809265847992320.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: #05a660;\" name=\"7OChO7L3MK7O.0.4809265847992320\" type=\"radio\" data-index=\"0\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"7OChO7L3MK7O.0.4809265847992320.0\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"7OChO7L3MK7O.0.4809265847992320.0\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2211\ufffd=138\ufffd\ufffd\u00d7(0.77)\ufffd\u00d7(0.23)8\u2212\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mop\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mop op-symbol small-op\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Size1; border-color: currentcolor; position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.954008em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.40029em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><span class=\"mrel mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.2029em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">8<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07153em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">C<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.311664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.07153em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00d7<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.77<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.824664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00d7<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.23<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.824664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">8<\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"7OChO7L3MK7O.0.4809265847992320.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: #05a660;\" name=\"7OChO7L3MK7O.0.4809265847992320\" type=\"radio\" data-index=\"1\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"7OChO7L3MK7O.0.4809265847992320.1\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"7OChO7L3MK7O.0.4809265847992320.1\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2211\ufffd=038\ufffd\ufffd\u00d7(0.77)\ufffd\u00d7(0.23)8\u2212\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mop\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mop op-symbol small-op\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Size1; border-color: currentcolor; position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.954008em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.40029em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><span class=\"mrel mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.2029em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">8<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07153em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">C<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.311664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.07153em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00d7<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.77<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.824664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00d7<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.23<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.824664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">8<\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"7OChO7L3MK7O.0.4809265847992320.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: #05a660;\" name=\"7OChO7L3MK7O.0.4809265847992320\" type=\"radio\" data-index=\"2\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"7OChO7L3MK7O.0.4809265847992320.2\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"7OChO7L3MK7O.0.4809265847992320.2\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2211\ufffd=048\ufffd\ufffd\u00d7(0.77)\ufffd\u00d7(0.23)8\u2212\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mop\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mop op-symbol small-op\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Size1; border-color: currentcolor; position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.954008em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.40029em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><span class=\"mrel mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.2029em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">8<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07153em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">C<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.311664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.07153em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00d7<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.77<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.824664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00d7<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.23<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.824664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">8<\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"7OChO7L3MK7O.0.4809265847992320.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: #05a660;\" name=\"7OChO7L3MK7O.0.4809265847992320\" type=\"radio\" data-index=\"3\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"7OChO7L3MK7O.0.4809265847992320.3\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"7OChO7L3MK7O.0.4809265847992320.3\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\u2211\ufffd=148\ufffd\ufffd\u00d7(0.77)\ufffd\u00d7(0.23)8\u2212\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mop\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mop op-symbol small-op\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Size1; border-color: currentcolor; position: relative; top: -5e-06em;\">\u2211<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.954008em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.40029em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><span class=\"mrel mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.2029em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">8<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07153em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">C<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.311664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.07153em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00d7<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.77<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.824664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u00d7<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.23<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.824664em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">8<\/span><span class=\"mbin mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2212<\/span><span class=\"mord mathnormal mtight\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><p>\u00a0<\/p><div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"Wa68ekm0Fqr7\" class=\"qt-mc-question qt-standalone\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div>If\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd\u223c\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd\ufffd(\ufffd,\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u223c<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05017em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">B<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">in<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">o<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">mia<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.01968em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">l<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">n<\/span><span class=\"mpunct\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">,<\/span><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">p<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>, then which of the following statement\/s is\/are always true? (<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd&gt;0<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">n<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&gt;<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><\/span><\/span><\/span><\/span>\u00a0and\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">0&lt;\ufffd&lt;1<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&lt;<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">p<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&lt;<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span>)<div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"Wa68ekm0Fqr7.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"Wa68ekm0Fqr7\" type=\"checkbox\" data-index=\"0\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"Wa68ekm0Fqr7.0\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"Wa68ekm0Fqr7.0\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)\u2264\ufffd\ufffd\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">E<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2264<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Va<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.02778em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">r<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"Wa68ekm0Fqr7.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"Wa68ekm0Fqr7\" type=\"checkbox\" data-index=\"1\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"Wa68ekm0Fqr7.1\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"Wa68ekm0Fqr7.1\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)&lt;\ufffd\ufffd\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">E<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&lt;<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Va<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.02778em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">r<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"Wa68ekm0Fqr7.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"Wa68ekm0Fqr7\" type=\"checkbox\" data-index=\"2\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"Wa68ekm0Fqr7.2\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"Wa68ekm0Fqr7.2\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)\u2265\ufffd\ufffd\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">E<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2265<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Va<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.02778em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">r<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"Wa68ekm0Fqr7.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"Wa68ekm0Fqr7\" type=\"checkbox\" data-index=\"3\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"Wa68ekm0Fqr7.3\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"Wa68ekm0Fqr7.3\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)&gt;\ufffd\ufffd\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">E<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">&gt;<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Va<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.02778em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">r<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"Wa68ekm0Fqr7.4\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"Wa68ekm0Fqr7\" type=\"checkbox\" data-index=\"4\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"Wa68ekm0Fqr7.4\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"Wa68ekm0Fqr7.4\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd\ufffd\ufffd(\ufffd)\u2264\ufffd.\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Va<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.02778em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">r<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2264<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">S<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">.<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.02778em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">D<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"Wa68ekm0Fqr7.5\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"Wa68ekm0Fqr7\" type=\"checkbox\" data-index=\"5\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"Wa68ekm0Fqr7.5\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"Wa68ekm0Fqr7.5\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd\ufffd\ufffd(\ufffd)\u2265\ufffd.\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">Va<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.02778em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">r<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">\u2265<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">S<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">.<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.02778em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">D<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><\/div><p>\u00a0<\/p><div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div id=\"hwkDJI88YmGN\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"hwkDJI88YmGN.0.4726232319000576\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div>Two friends (say &#8216;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">A<\/span><\/span><\/span><\/span><\/span>&#8216; and &#8216;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05017em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">B<\/span><\/span><\/span><\/span><\/span>&#8216;) could not decide whether to play a racing game or a boxing game on Xbox. They decide to play a card-game first. If &#8216;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">A<\/span><\/span><\/span><\/span><\/span>&#8216; wins at least 3 rounds out of the 5 rounds of the card game played, then the boxing game will be played. The chances of &#8216;<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">A<\/span><\/span><\/span><\/span><\/span>&#8216; winning in any round of the card game is 2:5. Find the probability that the boxing game will be played on Xbox? (Enter the answer correct to 2 decimal places)<br style=\"margin: 0px; padding: 0px;\" \/><span style=\"margin: 0px; padding: 0px; font-weight: bolder;\">Hint:<\/span>\u00a0If the chances of happening of an event is x:y then, the probability equals\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd\ufffd+\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.10756em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">x<\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.03588em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">y<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">x<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><input id=\"qt-response-num-id-hwkDJI88YmGN.0.4726232319000576\" style=\"margin-top: 12px; margin-bottom: 8px; padding-top: 2px; padding-bottom: 2px; font-family: inherit; font-size: inherit; width: 1011.36px; border-width: 0px 0px 1px; border-top-style: initial; border-right-style: initial; border-left-style: initial; border-color: #05a660;\" step=\"any\" type=\"number\" \/><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><p>\u00a0<\/p><div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div id=\"4zsBuGPvrxuT\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"4zsBuGPvrxuT.0.6524592352919552\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div>Let\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><\/span><\/span><\/span><\/span>~ Binomial(6,p). If the probabilities of 4 and 5 successes are approximately 0.311 and, 0.1866 respectively, then find the parameter &#8216;p&#8217; of the distribution.(Enter the answer correct to 2 decimal places)<div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><input id=\"qt-response-num-id-4zsBuGPvrxuT.0.6524592352919552\" style=\"margin-top: 12px; margin-bottom: 8px; padding-top: 2px; padding-bottom: 2px; font-family: inherit; font-size: inherit; width: 1011.36px; border-width: 0px 0px 1px; border-top-style: initial; border-right-style: initial; border-left-style: initial; border-color: #05a660;\" step=\"any\" type=\"number\" \/><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><p>\u00a0<\/p><div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div id=\"PdglbRaoFlX0\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"PdglbRaoFlX0.0.4968010590715904\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div>If the expected number of sixes hit by a batsman on\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">n<\/span><\/span><\/span><\/span><\/span>\u00a0balls is 6.39 and the variance for the same is 1.8531, then what is the probability of him hitting at least one six on any randomly selected\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">n<\/span><\/span><\/span><\/span><\/span>\u00a0balls? Assume that the probability of him hitting a six on any ball is constant. (Enter the answer correct to 4 decimal places)<div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><input id=\"qt-response-num-id-PdglbRaoFlX0.0.4968010590715904\" style=\"margin-top: 12px; margin-bottom: 8px; padding-top: 2px; padding-bottom: 2px; font-family: inherit; font-size: inherit; width: 1011.36px; border-width: 0px 0px 1px; border-top-style: initial; border-right-style: initial; border-left-style: initial; border-color: #05a660;\" step=\"any\" type=\"number\" \/><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><p>\u00a0<\/p><div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div id=\"QoRRtWxVh9gj\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"QoRRtWxVh9gj.0.5666546085003264\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div>The probability of a student clearing a competitive exam is\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">14<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">4<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>. If he gives the exam 6 times, then what is the probability of him clearing the exam at least twice?(Enter the answer correct to 2 decimal places)<div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><input id=\"qt-response-num-id-QoRRtWxVh9gj.0.5666546085003264\" style=\"margin-top: 12px; margin-bottom: 8px; padding-top: 2px; padding-bottom: 2px; font-family: inherit; font-size: inherit; width: 1011.36px; border-width: 0px 0px 1px; border-top-style: initial; border-right-style: initial; border-left-style: initial; border-color: #05a660;\" step=\"any\" type=\"number\" \/><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><p>\u00a0<\/p><div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"z0csLNJBq3Zs\" class=\"qt-mc-question qt-standalone\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">Choose the correct condition\/s about binomial distribution.<\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"z0csLNJBq3Zs.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"z0csLNJBq3Zs\" type=\"checkbox\" data-index=\"0\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"z0csLNJBq3Zs.0\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"z0csLNJBq3Zs.0\">The probability of success\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">p<\/span><\/span><\/span><\/span><\/span>\u00a0keeps varying for each trial.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"z0csLNJBq3Zs.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"z0csLNJBq3Zs\" type=\"checkbox\" data-index=\"1\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"z0csLNJBq3Zs.1\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"z0csLNJBq3Zs.1\">The number of trials\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">n<\/span><\/span><\/span><\/span><\/span>\u00a0is finite.<\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"z0csLNJBq3Zs.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"z0csLNJBq3Zs\" type=\"checkbox\" data-index=\"2\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"z0csLNJBq3Zs.2\">The trials are dependent on each other.<\/label><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"z0csLNJBq3Zs.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit;\" name=\"z0csLNJBq3Zs\" type=\"checkbox\" data-index=\"3\" \/><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"z0csLNJBq3Zs.3\">The trials are independent of each other.<\/label><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><\/div><p>\u00a0<\/p><div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div id=\"iECRWzaL7wIH\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"iECRWzaL7wIH.0.6498115708256256\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div>Rithika wants to test whether the coin she has is a fair coin or not. To test this, she conducted an experiment of tossing the coin 5 times. Binomial random variable\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><\/span><\/span><\/span><\/span>\u00a0is defined as the total number of heads(<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><\/span>) after 5 tosses. The probability distribution of the binomial random variable is given in Table 11.1.G.<center style=\"margin: 0px; padding: 0px;\"><table class=\"content-table\" style=\"margin-top: 25px; margin-bottom: 25px; padding: 0px; caption-side: bottom; border-collapse: collapse; font-size: 0.9em; min-width: 400px; border-radius: 5px 5px 0px 0px; overflow: hidden; box-shadow: rgba(0, 0, 0, 0.15) 0px 0px 20px;\"><thead style=\"margin: 0px; padding: 0px; border-width: 0px; border-image: initial;\"><tr style=\"margin: 0px; padding: 0px; border-width: 0px; border-image: initial; background-color: #009879; color: #ffffff; font-weight: bold;\"><th style=\"margin: 0px; padding: 12px 15px; text-align: center; border-color: inherit; border-width: 0px; border-image: initial;\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd=\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><\/span><\/span><\/span><\/span><\/th><th style=\"margin: 0px; padding: 12px 15px; text-align: center; border-color: inherit; border-width: 0px; border-image: initial;\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-weight: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd=\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.13889em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">P<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">i<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span><\/th><\/tr><\/thead><tbody style=\"margin: 0px; padding: 0px; border-width: 0px; border-image: initial;\"><tr style=\"margin: 0px; padding: 0px; border-width: 0px 0px 1px; border-bottom-style: solid; border-bottom-color: #dddddd; border-image: initial;\"><td style=\"margin: 0px; padding: 12px 15px; border-color: inherit; border-bottom-style: solid; border-width: 0px; border-image: initial; text-align: center;\">0<\/td><td style=\"margin: 0px; padding: 12px 15px; border-color: inherit; border-bottom-style: solid; border-width: 0px; border-image: initial; text-align: center;\">0.00032<\/td><\/tr><tr style=\"margin: 0px; padding: 0px; border-width: 0px 0px 1px; border-bottom-style: solid; border-bottom-color: #dddddd; border-image: initial;\"><td style=\"margin: 0px; padding: 12px 15px; border-color: inherit; border-bottom-style: solid; border-width: 0px; border-image: initial; text-align: center;\">1<\/td><td style=\"margin: 0px; padding: 12px 15px; border-color: inherit; border-bottom-style: solid; border-width: 0px; border-image: initial; text-align: center;\">0.0064<\/td><\/tr><tr style=\"margin: 0px; padding: 0px; border-width: 0px 0px 1px; border-bottom-style: solid; border-bottom-color: #dddddd; border-image: initial;\"><td style=\"margin: 0px; padding: 12px 15px; border-color: inherit; border-bottom-style: solid; border-width: 0px; border-image: initial; text-align: center;\">2<\/td><td style=\"margin: 0px; padding: 12px 15px; border-color: inherit; border-bottom-style: solid; border-width: 0px; border-image: initial; text-align: center;\">0.0512<\/td><\/tr><tr style=\"margin: 0px; padding: 0px; border-width: 0px 0px 1px; border-bottom-style: solid; border-bottom-color: #dddddd; border-image: initial;\"><td style=\"margin: 0px; padding: 12px 15px; border-color: inherit; border-bottom-style: solid; border-width: 0px; border-image: initial; text-align: center;\">3<\/td><td style=\"margin: 0px; padding: 12px 15px; border-color: inherit; border-bottom-style: solid; border-width: 0px; border-image: initial; text-align: center;\">0.2048<\/td><\/tr><tr style=\"margin: 0px; padding: 0px; border-width: 0px 0px 1px; border-bottom-style: solid; border-bottom-color: #dddddd; border-image: initial;\"><td style=\"margin: 0px; padding: 12px 15px; border-color: inherit; border-bottom-style: solid; border-width: 0px; border-image: initial; text-align: center;\">4<\/td><td style=\"margin: 0px; padding: 12px 15px; border-color: inherit; border-bottom-style: solid; border-width: 0px; border-image: initial; text-align: center;\">0.4096<\/td><\/tr><tr style=\"margin: 0px; padding: 0px; border-width: 0px 0px 2px; border-bottom-style: solid; border-bottom-color: #009879; border-image: initial;\"><td style=\"margin: 0px; padding: 12px 15px; border-color: inherit; border-bottom-style: solid; border-width: 0px; border-image: initial; text-align: center;\">5<\/td><td style=\"margin: 0px; padding: 12px 15px; border-color: inherit; border-bottom-style: solid; border-width: 0px; border-image: initial; text-align: center;\">0.32768<\/td><\/tr><\/tbody><caption style=\"margin: 0px; padding: 0.5rem 0px; color: #6c757d; text-align: left;\" align=\"bottom\">Table 11.1.G: Binomial Distribution<\/caption><\/table><\/center>What is the approximate probability of getting a head in tossing the given coin? (Enter the answer correct to one decimal place)<div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><input id=\"qt-response-num-id-iECRWzaL7wIH.0.6498115708256256\" style=\"margin-top: 12px; margin-bottom: 8px; padding-top: 2px; padding-bottom: 2px; font-family: inherit; font-size: inherit; width: 1011.36px; border-width: 0px 0px 1px; border-top-style: initial; border-right-style: initial; border-left-style: initial; border-color: #05a660;\" step=\"any\" type=\"number\" \/><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><p>\u00a0<\/p><div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div id=\"HpAZ07NK6u0X\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"HpAZ07NK6u0X.0.4674180268163072\" class=\"qt-mc-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">At a school function, It is noticed that 9% of the students are not wearing polished shoes and 12% of students are not wearing school ties. It is announced that the students who have committed any of the infractions will be punished, and that these two infractions are independent of one another. If a teacher selects 5 students at random, then find the probability that exactly three of the students will be punished for any of the infractions?<\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"HpAZ07NK6u0X.0.4674180268163072.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: #05a660;\" name=\"HpAZ07NK6u0X.0.4674180268163072\" type=\"radio\" data-index=\"0\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"HpAZ07NK6u0X.0.4674180268163072.0\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"HpAZ07NK6u0X.0.4674180268163072.0\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">5\ufffd3(0.1992)3(0.8008)2<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07153em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">C<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.07153em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.1992<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.8008<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"HpAZ07NK6u0X.0.4674180268163072.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: #05a660;\" name=\"HpAZ07NK6u0X.0.4674180268163072\" type=\"radio\" data-index=\"1\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"HpAZ07NK6u0X.0.4674180268163072.1\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"HpAZ07NK6u0X.0.4674180268163072.1\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">5\ufffd3(0.0108)3(0.9892)2<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07153em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">C<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.07153em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.0108<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.9892<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"HpAZ07NK6u0X.0.4674180268163072.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: #05a660;\" name=\"HpAZ07NK6u0X.0.4674180268163072\" type=\"radio\" data-index=\"2\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"HpAZ07NK6u0X.0.4674180268163072.2\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"HpAZ07NK6u0X.0.4674180268163072.2\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">5\ufffd3(0.09)3(0.91)2+5\ufffd3(0.12)3(0.88)2<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07153em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">C<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.07153em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.09<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.91<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">+<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07153em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">C<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.07153em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.12<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.88<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"HpAZ07NK6u0X.0.4674180268163072.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: #05a660;\" name=\"HpAZ07NK6u0X.0.4674180268163072\" type=\"radio\" data-index=\"3\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"HpAZ07NK6u0X.0.4674180268163072.3\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"HpAZ07NK6u0X.0.4674180268163072.3\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">5\ufffd3(0.21)3(0.79)2<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">5<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07153em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">C<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.301108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px -0.07153em; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.55em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.21<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">0.79<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><span class=\"msupsub\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 0.814108em;\"><span class=\"\" style=\"margin: 0px 0.05em 0px 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.063em;\"><span class=\"sizing reset-size6 size3 mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block; font-size: 0.7em;\"><span class=\"mord mtight\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><p>\u00a0<\/p><div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div id=\"FSUwEu1T1ZLJ\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">\u00a0<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"FSUwEu1T1ZLJ.0.5237130221584384\" class=\"qt-mc-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">There are 7 black and 20 blue pens in a box. A pen is chosen at random, and its colour is noted. If the process repeats independently, 13 times with replacement, then calculate the expected number of black pens chosen?<\/div><div class=\"qt-choices\" style=\"margin: 16px 0px 0px; padding: 0px;\"><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"FSUwEu1T1ZLJ.0.5237130221584384.0\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: #05a660;\" name=\"FSUwEu1T1ZLJ.0.5237130221584384\" type=\"radio\" data-index=\"0\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"FSUwEu1T1ZLJ.0.5237130221584384.0\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"FSUwEu1T1ZLJ.0.5237130221584384.0\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">9127<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">27<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">91<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"FSUwEu1T1ZLJ.0.5237130221584384.1\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: #05a660;\" name=\"FSUwEu1T1ZLJ.0.5237130221584384\" type=\"radio\" data-index=\"1\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"FSUwEu1T1ZLJ.0.5237130221584384.1\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"FSUwEu1T1ZLJ.0.5237130221584384.1\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">26027<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">27<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">260<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"FSUwEu1T1ZLJ.0.5237130221584384.2\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: #05a660;\" name=\"FSUwEu1T1ZLJ.0.5237130221584384\" type=\"radio\" data-index=\"2\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"FSUwEu1T1ZLJ.0.5237130221584384.2\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"FSUwEu1T1ZLJ.0.5237130221584384.2\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">16920<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">20<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">169<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"gcb-mcq-choice\" style=\"margin: 0px 0px 18px; padding: 0px; display: flex; align-items: center;\"><input id=\"FSUwEu1T1ZLJ.0.5237130221584384.3\" style=\"padding: 0px; font-family: inherit; font-size: inherit; width: 15px; height: 15px; background-color: #05a660;\" name=\"FSUwEu1T1ZLJ.0.5237130221584384\" type=\"radio\" data-index=\"3\" \/><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"FSUwEu1T1ZLJ.0.5237130221584384.3\"><label style=\"margin: 0px 0px 0px 16px; padding: 0px;\" for=\"FSUwEu1T1ZLJ.0.5237130221584384.3\"><span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">9120<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"mfrac\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\"><span class=\"vlist-t vlist-t2\" style=\"margin: 0px -2px 0px 0px; padding: 0px; border-color: currentcolor; border-collapse: collapse; display: inline-table; table-layout: fixed;\"><span class=\"vlist-r\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-row; text-align: center;\"><span class=\"vlist\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: table-cell; position: relative; vertical-align: bottom; height: 1.32144em;\"><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -2.314em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">20<\/span><\/span><\/span><span class=\"\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: block; height: 0px; position: relative; top: -3.677em;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">91<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/label><\/label><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><\/div><p>\u00a0<\/p><div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"X7iu8fZJPcbY\" class=\"qt-sa-question qt-standalone\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\">Number of calls received at an office follows a Poisson distribution with an average of 1 call per minute. Find the probability that no call will be received in two minutes at the office. (Enter the answer correct to 2 decimal accuracy.)<\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><input id=\"qt-response-num-id-X7iu8fZJPcbY\" style=\"margin-top: 12px; margin-bottom: 8px; padding-top: 2px; padding-bottom: 2px; font-family: inherit; font-size: inherit; width: 1011.36px; border-width: 0px 0px 1px; border-top-style: initial; border-right-style: initial; border-left-style: initial; border-color: #05a660;\" step=\"any\" type=\"number\" \/><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><\/div><p>\u00a0<\/p><div style=\"margin: 0px; padding: 0px; font-family: sans-serif;\"><div id=\"xSAAwvO0Yd6l\" class=\"qt-question-group\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-introduction\" style=\"margin: 0px 0px 8px; padding: 0px; font-size: 1.6rem;\">A quiz team is to be chosen randomly from 6 boys and 4 girls. The team has 3 slots which are to be filled randomly. If\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><\/span><\/span><\/span><\/span>\u00a0denotes the number of boys in the quiz team, then using the given information, answer questions (12) and (13).<\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"xSAAwvO0Yd6l.0.5329626599522304\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div>Calculate\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd=2)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.13889em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">P<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mrel\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">=<\/span><\/span><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">2<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>. (Enter the answer correct to 2 decimal places)<div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div class=\"qt-response\" style=\"margin: 0px; padding: 0px;\"><input id=\"qt-response-num-id-xSAAwvO0Yd6l.0.5329626599522304\" style=\"margin-top: 12px; margin-bottom: 8px; padding-top: 2px; padding-bottom: 2px; font-family: inherit; font-size: inherit; width: 1011.36px; border-width: 0px 0px 1px; border-top-style: initial; border-right-style: initial; border-left-style: initial; border-color: #05a660;\" step=\"any\" type=\"number\" \/><\/div><div class=\"qt-feedback qt-hidden\" style=\"margin: 0px; padding: 0px;\" role=\"alert\">\u00a0<\/div><\/div><div class=\"qt-points\" style=\"margin: 0px; padding: 0px; float: right; font-weight: bold; text-align: right;\"><em style=\"margin: 0px; padding: 0px;\">1 point<\/em><\/div><\/div><div class=\"gcb-cols gcb-question-counter-increment gcb-question-row\" style=\"margin: 0px 0px 16px; padding: 2rem; counter-increment: question-number 1; box-shadow: #e1e1e1 1px 1px 1px;\"><div class=\"gcb-col-counters gcb-show-question-counter\" style=\"margin: 0px; padding: 0px 5px 0px 0px; float: left;\">\u00a0<\/div><div id=\"xSAAwvO0Yd6l.1.6543406637514752\" class=\"qt-sa-question qt-embedded\" style=\"margin: 0px; padding: 0px;\"><div class=\"qt-question\" style=\"margin: 0px; padding: 0px; color: rgba(0, 0, 0, 0.87); font-size: 14px;\"><div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div>Calculate the value of\u00a0<span class=\"inline-equation\" style=\"margin: 0px; padding: 0px;\"><span class=\"katex\" style=\"margin: 0px; padding: 0px; font-variant-numeric: normal; font-variant-east-asian: normal; font-variant-alternates: normal; font-kerning: auto; font-optical-sizing: auto; font-feature-settings: normal; font-variation-settings: normal; font-stretch: normal; font-size: 1.21em; line-height: 1.2; font-family: KaTeX_Main, 'Times New Roman', serif; text-rendering: auto;\"><span class=\"katex-mathml\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border: 0px; clip: rect(1px, 1px, 1px, 1px); height: 1px; overflow: hidden; position: absolute; width: 1px;\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" style=\"margin: 0px; padding: 0px; font-family: sans-serif; border-color: currentcolor;\" aria-hidden=\"true\"><span class=\"base\" style=\"margin: 0px; padding: 0px; border-color: currentcolor; position: relative; text-wrap: nowrap; width: min-content; display: inline-block;\"><span class=\"mord mathnormal\" style=\"margin: 0px 0.05764em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">E<\/span><span class=\"mopen\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">(<\/span><span class=\"mord mathnormal\" style=\"margin: 0px 0.07847em 0px 0px; padding: 0px; font-family: KaTeX_Math; border-color: currentcolor; font-style: italic;\">X<\/span><span class=\"mclose\" style=\"margin: 0px; padding: 0px; border-color: currentcolor;\">)<\/span><\/span><\/span><\/span><\/span>. (Enter the answer correct to 2 decimal places)<div style=\"margin: 0px; padding: 0px;\">\u00a0<\/div><\/div><div>\u00a0<\/div><\/div><\/div><\/div><\/div>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Statistics week 11 graded assignment Complete&nbsp; Solutions Are Discussed In This Blog We Hope This Might Help You All In Matching Answers . Or For Some Others Reasons Not Able To Complete Graded Assignments&nbsp; A match predictor claims that he can predict the result of a match correctly 77% of the time. It is agreed&hellip;&nbsp;<a href=\"https:\/\/iitmadrasstudentscommunity.me\/statistics-week-11-graded-assignments-iit-madras\/\" class=\"\" rel=\"bookmark\">Read More &raquo;<span class=\"screen-reader-text\">Statistics Week 11 Graded Assignments IIT Madras<\/span><\/a><\/p>\n","protected":false},"author":4,"featured_media":1197,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"","neve_meta_content_width":0,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":"","neve_meta_reading_time":"","_themeisle_gutenberg_block_has_review":false,"_ti_tpc_template_sync":false,"_ti_tpc_template_id":"","footnotes":""},"categories":[10],"tags":[79],"_links":{"self":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts\/1209"}],"collection":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/comments?post=1209"}],"version-history":[{"count":5,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts\/1209\/revisions"}],"predecessor-version":[{"id":1214,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/posts\/1209\/revisions\/1214"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/media\/1197"}],"wp:attachment":[{"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/media?parent=1209"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/categories?post=1209"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/iitmadrasstudentscommunity.me\/wp-json\/wp\/v2\/tags?post=1209"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}