{"id":258143,"date":"2025-07-17T22:19:16","date_gmt":"2025-07-17T22:19:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=258143"},"modified":"2025-07-17T22:19:20","modified_gmt":"2025-07-17T22:19:20","slug":"maria-is-playing-a-game-of-chance-in-which-she-rolls-a-number-cube-with-sides-numbered-from-1-to-6","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/17\/maria-is-playing-a-game-of-chance-in-which-she-rolls-a-number-cube-with-sides-numbered-from-1-to-6\/","title":{"rendered":"Maria is playing a game of chance in which she rolls a number cube with sides numbered from 1 to 6 ."},"content":{"rendered":"\n<p>Maria is playing a game of chance in which she rolls a number cube with sides numbered from 1 to 6 . The number cube is fair, so a side is rolled at random. This game is this: Maria rolls the number cube once. She wins $1 if a 1 is rolled, $2 if a 2 is rolled, $3 if a 3 is rolled, and $4 if a 4 is rolled. She loses $2.75 if a 5 or 6 is rolled.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To calculate the expected value of Maria&#8217;s game, we need to account for all possible outcomes and their corresponding probabilities.<\/p>\n\n\n\n<p>The game has 6 possible outcomes, one for each side of the number cube, each with an equal probability of 16\\frac{1}{6}61\u200b. The outcomes and their associated winnings (or losses) are as follows:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Rolling a 1:<\/strong> Maria wins $1.<\/li>\n\n\n\n<li><strong>Rolling a 2:<\/strong> Maria wins $2.<\/li>\n\n\n\n<li><strong>Rolling a 3:<\/strong> Maria wins $3.<\/li>\n\n\n\n<li><strong>Rolling a 4:<\/strong> Maria wins $4.<\/li>\n\n\n\n<li><strong>Rolling a 5 or 6:<\/strong> Maria loses $2.75 (each of these two outcomes has a probability of 16\\frac{1}{6}61\u200b).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Calculate the expected value<\/h3>\n\n\n\n<p>The expected value (EV) is a weighted average of all possible outcomes, where each outcome is multiplied by its probability. The formula for expected value is:EV=\u2211(outcome\u00d7probability&nbsp;of&nbsp;that&nbsp;outcome)EV = \\sum (\\text{outcome} \\times \\text{probability of that outcome})EV=\u2211(outcome\u00d7probability&nbsp;of&nbsp;that&nbsp;outcome)<\/p>\n\n\n\n<p>Let&#8217;s calculate it for each outcome:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For rolling a 1:<\/li>\n<\/ul>\n\n\n\n<p>1\u00d716=161 \\times \\frac{1}{6} = \\frac{1}{6}1\u00d761\u200b=61\u200b<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For rolling a 2:<\/li>\n<\/ul>\n\n\n\n<p>2\u00d716=262 \\times \\frac{1}{6} = \\frac{2}{6}2\u00d761\u200b=62\u200b<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For rolling a 3:<\/li>\n<\/ul>\n\n\n\n<p>3\u00d716=363 \\times \\frac{1}{6} = \\frac{3}{6}3\u00d761\u200b=63\u200b<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For rolling a 4:<\/li>\n<\/ul>\n\n\n\n<p>4\u00d716=464 \\times \\frac{1}{6} = \\frac{4}{6}4\u00d761\u200b=64\u200b<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For rolling a 5:<\/li>\n<\/ul>\n\n\n\n<p>\u22122.75\u00d716=\u22122.756-2.75 \\times \\frac{1}{6} = -\\frac{2.75}{6}\u22122.75\u00d761\u200b=\u221262.75\u200b<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For rolling a 6:<\/li>\n<\/ul>\n\n\n\n<p>\u22122.75\u00d716=\u22122.756-2.75 \\times \\frac{1}{6} = -\\frac{2.75}{6}\u22122.75\u00d761\u200b=\u221262.75\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Sum all the contributions<\/h3>\n\n\n\n<p>Now, let&#8217;s add these up to find the total expected value:EV=16+26+36+46+(\u22122.756)+(\u22122.756)EV = \\frac{1}{6} + \\frac{2}{6} + \\frac{3}{6} + \\frac{4}{6} + \\left(-\\frac{2.75}{6}\\right) + \\left(-\\frac{2.75}{6}\\right)EV=61\u200b+62\u200b+63\u200b+64\u200b+(\u221262.75\u200b)+(\u221262.75\u200b)<\/p>\n\n\n\n<p>Simplifying:EV=1+2+3+4\u22122.75\u22122.756EV = \\frac{1 + 2 + 3 + 4 &#8211; 2.75 &#8211; 2.75}{6}EV=61+2+3+4\u22122.75\u22122.75\u200bEV=7.56=1.25EV = \\frac{7.5}{6} = 1.25EV=67.5\u200b=1.25<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p>The expected value of Maria&#8217;s game is <strong>$1.25<\/strong>. This means that, on average, Maria can expect to win $1.25 each time she plays the game.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-881.jpeg\" alt=\"\" class=\"wp-image-258144\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Maria is playing a game of chance in which she rolls a number cube with sides numbered from 1 to 6 . The number cube is fair, so a side is rolled at random. This game is this: Maria rolls the number cube once. She wins $1 if a 1 is rolled, $2 if a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-258143","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258143","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=258143"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/258143\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=258143"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=258143"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=258143"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}