{"id":225669,"date":"2025-06-04T11:27:35","date_gmt":"2025-06-04T11:27:35","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225669"},"modified":"2025-06-04T11:27:37","modified_gmt":"2025-06-04T11:27:37","slug":"compare-the-rules-of-two-games","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/compare-the-rules-of-two-games\/","title":{"rendered":"Compare the rules of two games"},"content":{"rendered":"\n<p>Compare the rules of two games. Game A: Two six-sided dice are thrown. The numbers on the dice determine which player gets a point. Player 1 gets a point if the product of the numbers on the dice is even. Player 2 gets a point if the product is odd. Game B: Two six-sided dice are thrown. The numbers on the dice determine which player gets a point. Player 1 gets a point if the sum of the numbers on the dice is even. Player 2 gets a point if the sum is odd. Which statement accurately describes whether these games are fair?<\/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><strong>Correct Answer:<\/strong><br><strong>Game A is not fair; Game B is fair.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Explanation (300 words):<\/strong><\/p>\n\n\n\n<p>To determine whether the games are fair, we must examine the probability of each player winning in both games. A game is fair if all players have an equal probability of winning, i.e., each has a 50% chance.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Game A: Product-Based Rules<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Player 1 scores if the product of the two dice is <strong>even<\/strong>.<\/li>\n\n\n\n<li>Player 2 scores if the product is <strong>odd<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>Recall:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>An <strong>odd product<\/strong> occurs only if <strong>both dice roll odd numbers<\/strong>.<\/li>\n\n\n\n<li>The odd numbers on a die are 1, 3, and 5 \u2014 so each die has a 3\/6 = 1\/2 chance of being odd.<\/li>\n\n\n\n<li>The probability that <strong>both dice<\/strong> show odd numbers = (1\/2) \u00d7 (1\/2) = <strong>1\/4<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>Thus:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Probability product is <strong>odd<\/strong> (Player 2 scores) = <strong>1\/4<\/strong>.<\/li>\n\n\n\n<li>Probability product is <strong>even<\/strong> (Player 1 scores) = <strong>1 \u2013 1\/4 = 3\/4<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>\u27a1\ufe0f <strong>Game A is not fair<\/strong>, because Player 1 has a <strong>75% chance<\/strong> of scoring, while Player 2 only has <strong>25%<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Game B: Sum-Based Rules<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Player 1 scores if the sum is <strong>even<\/strong>.<\/li>\n\n\n\n<li>Player 2 scores if the sum is <strong>odd<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>Let\u2019s examine the probabilities:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A sum is <strong>even<\/strong> if both dice are even or both are odd.<\/li>\n\n\n\n<li>A sum is <strong>odd<\/strong> if one die is even and the other is odd.<\/li>\n<\/ul>\n\n\n\n<p>Each die has 3 odd and 3 even numbers.<br>So:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P(even, even) = (1\/2) \u00d7 (1\/2) = 1\/4<\/li>\n\n\n\n<li>P(odd, odd) = (1\/2) \u00d7 (1\/2) = 1\/4<\/li>\n\n\n\n<li>P(one even, one odd) = 1 \u2013 (1\/4 + 1\/4) = 1\/2<\/li>\n<\/ul>\n\n\n\n<p>Thus:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Probability sum is even = 1\/4 + 1\/4 = <strong>1\/2<\/strong><\/li>\n\n\n\n<li>Probability sum is odd = <strong>1\/2<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\u27a1\ufe0f <strong>Game B is fair<\/strong>, as both players have a <strong>50% chance<\/strong> of winning.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Conclusion:<\/strong><br>Game A is biased in favor of Player 1, while Game B gives both players an equal chance \u2014 it is fair.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner9-45.jpeg\" alt=\"\" class=\"wp-image-225670\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Compare the rules of two games. Game A: Two six-sided dice are thrown. The numbers on the dice determine which player gets a point. Player 1 gets a point if the product of the numbers on the dice is even. Player 2 gets a point if the product is odd. Game B: Two six-sided dice [&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-225669","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225669","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=225669"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225669\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225669"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225669"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}