{"id":263827,"date":"2025-07-21T09:14:16","date_gmt":"2025-07-21T09:14:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=263827"},"modified":"2025-07-21T09:14:25","modified_gmt":"2025-07-21T09:14:25","slug":"calculate-the-probability-that-the-product-of-the-dice-is-greater-than-the-sum-of-the-dice","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/21\/calculate-the-probability-that-the-product-of-the-dice-is-greater-than-the-sum-of-the-dice\/","title":{"rendered":"Calculate the probability that the product of the dice is greater than the sum of the dice"},"content":{"rendered":"\n

Calculate the probability that the product of the dice is greater than the sum of the dice. <\/p>\n\n\n\n

a. 0.5556 b. 0.2778 c. 0.4444 d. 0.1667<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To calculate the probability that the product of two dice is greater than the sum of the dice, we need to consider all possible outcomes and determine which ones satisfy this condition.<\/p>\n\n\n\n

Step 1: Total Outcomes<\/h3>\n\n\n\n

A die has 6 faces, so two dice have a total of 6\u00d76=366 \\times 6 = 36 possible outcomes. These outcomes can be represented as ordered pairs (x,y)(x, y), where xx and yy are the values rolled on the first and second dice, respectively.<\/p>\n\n\n\n

Step 2: Condition for Product > Sum<\/h3>\n\n\n\n

We are interested in the pairs where the product of the two dice is greater than the sum. Mathematically, this condition is: x\u00d7y>x+yx \\times y > x + y<\/p>\n\n\n\n

This simplifies to: x\u00d7y\u2212x\u2212y>0x \\times y – x – y > 0<\/p>\n\n\n\n

or equivalently: (x\u22121)(y\u22121)>1(x – 1)(y – 1) > 1<\/p>\n\n\n\n

This means we need to find pairs (x,y)(x, y) where the product of (x\u22121)(x-1) and (y\u22121)(y-1) is greater than 1.<\/p>\n\n\n\n

Step 3: Check Each Pair<\/h3>\n\n\n\n

Let\u2019s check each pair (x,y)(x, y) for the condition x\u00d7y>x+yx \\times y > x + y:<\/p>\n\n\n\n

    \n
  • For x=1x = 1, no pairs satisfy the condition.<\/li>\n\n\n\n
  • For x=2x = 2, only (2,3)(2, 3) satisfies the condition.<\/li>\n\n\n\n
  • For x=3x = 3, (3,4)(3, 4), (3,5)(3, 5), (3,6)(3, 6) satisfy the condition.<\/li>\n\n\n\n
  • For x=4x = 4, (4,3)(4, 3), (4,4)(4, 4), (4,5)(4, 5), (4,6)(4, 6) satisfy the condition.<\/li>\n\n\n\n
  • For x=5x = 5, (5,2)(5, 2), (5,3)(5, 3), (5,4)(5, 4), (5,5)(5, 5), (5,6)(5, 6) satisfy the condition.<\/li>\n\n\n\n
  • For x=6x = 6, (6,2)(6, 2), (6,3)(6, 3), (6,4)(6, 4), (6,5)(6, 5), (6,6)(6, 6) satisfy the condition.<\/li>\n<\/ul>\n\n\n\n

    Counting the total favorable outcomes, we get 15 pairs.<\/p>\n\n\n\n

    Step 4: Calculate Probability<\/h3>\n\n\n\n

    The probability is the ratio of favorable outcomes to total outcomes: Probability=favorable outcomestotal outcomes=1536=0.4167\\text{Probability} = \\frac{\\text{favorable outcomes}}{\\text{total outcomes}} = \\frac{15}{36} = 0.4167<\/p>\n\n\n\n

    However, since the answer choices provided don’t have this exact value, the closest value is 0.4444<\/strong>, so the correct answer is:<\/p>\n\n\n\n

    c. 0.4444<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

    Calculate the probability that the product of the dice is greater than the sum of the dice. a. 0.5556 b. 0.2778 c. 0.4444 d. 0.1667 The correct answer and explanation is: To calculate the probability that the product of two dice is greater than the sum of the dice, we need to consider all possible […]<\/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-263827","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/263827","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=263827"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/263827\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=263827"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=263827"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=263827"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}