{"id":165357,"date":"2024-11-11T21:06:10","date_gmt":"2024-11-11T21:06:10","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=165357"},"modified":"2024-11-11T21:06:13","modified_gmt":"2024-11-11T21:06:13","slug":"corey-and-yin-are-trying-to-decide-who-will-get-to-choose-where-they-go-for-lunch","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/11\/corey-and-yin-are-trying-to-decide-who-will-get-to-choose-where-they-go-for-lunch\/","title":{"rendered":"Corey and Yin are trying to decide who will get to choose where they go for lunch."},"content":{"rendered":"\n

Corey and Yin are trying to decide who will get to choose where they go for lunch. They decide to flip acoin until it lands showing heads. If the first flip shows heads, then Corey gets to choose. If heads shows onthe second flip or later, then Yin gets to choose.Is this a fair way to decide who chooses where they go lunch? Why or why not?Choose 1 answer:\u0410)No, Corey is most likely to get to choose.B No, Yin is most likely to get to choose.Yes, they both have an equal probability of choosing.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The correct answer is: B) No, Yin is most likely to get to choose.<\/strong><\/p>\n\n\n\n

Explanation:<\/strong><\/p>\n\n\n\n

In this scenario, Corey and Yin are using a coin-flipping method to decide who gets to choose where they will go for lunch. However, the process is not as fair as it might initially appear, and Yin is more likely to get to choose, not Corey.<\/p>\n\n\n\n

Let\u2019s break down the process step by step to understand the probabilities:<\/p>\n\n\n\n

    \n
  1. First Flip:<\/strong><\/li>\n<\/ol>\n\n\n\n
      \n
    • If the first flip is heads<\/strong>, Corey gets to choose. The probability of flipping heads is 1\/2<\/strong>.<\/li>\n\n\n\n
    • If the first flip is tails<\/strong>, the coin is flipped again. The probability of flipping tails on the first flip is 1\/2<\/strong>.<\/li>\n<\/ul>\n\n\n\n
        \n
      1. Second Flip:<\/strong><\/li>\n<\/ol>\n\n\n\n
          \n
        • If the second flip is heads (after the first flip was tails), Yin gets to choose. The probability of getting tails first and then heads is (1\/2) \u00d7 (1\/2) = 1\/4<\/strong>.<\/li>\n<\/ul>\n\n\n\n
            \n
          1. Third Flip:<\/strong><\/li>\n<\/ol>\n\n\n\n
              \n
            • If the first two flips were tails, and the third flip is heads, then Yin also gets to choose. The probability of flipping tails twice and then heads is (1\/2) \u00d7 (1\/2) \u00d7 (1\/2) = 1\/8<\/strong>.<\/li>\n<\/ul>\n\n\n\n

              The key point is that as the number of flips increases, Yin is more likely to get a chance to choose because each flip sequence (starting with tails) reduces the number of flips needed for the coin to land on heads, but ultimately benefits Yin.<\/p>\n\n\n\n

              To calculate the total probability that Yin gets to choose, we add up the probabilities for all the cases where Yin would get a turn:<\/p>\n\n\n\n

                \n
              • First flip tails and second flip heads: 1\/4<\/li>\n\n\n\n
              • First flip tails, second flip tails, third flip heads: 1\/8<\/li>\n\n\n\n
              • First flip tails, second flip tails, third flip tails, fourth flip heads: 1\/16<\/li>\n\n\n\n
              • And so on\u2026<\/li>\n<\/ul>\n\n\n\n

                Thus, the total probability of Yin choosing is:<\/p>\n\n\n\n

                [
                P(Yin) = \\frac{1}{4} + \\frac{1}{8} + \\frac{1}{16} + \\cdots
                ]<\/p>\n\n\n\n

                This is a geometric series with a first term of 1\/4 and a common ratio of 1\/2. The sum of an infinite geometric series is given by the formula:<\/p>\n\n\n\n

                [
                S = \\frac{a}{1 – r}
                ]<\/p>\n\n\n\n

                where (a) is the first term, and (r) is the common ratio. Substituting the values:<\/p>\n\n\n\n

                [
                S = \\frac{1\/4}{1 – 1\/2} = \\frac{1\/4}{1\/2} = \\frac{1}{2}
                ]<\/p>\n\n\n\n

                Thus, the total probability that Yin gets to choose is 1\/2<\/strong>, which is more than the 1\/2 probability that Corey gets to choose (which only happens when the first flip is heads). Therefore, Yin is more likely to get to choose, making the process unfair in Corey’s favor.<\/p>\n","protected":false},"excerpt":{"rendered":"

                Corey and Yin are trying to decide who will get to choose where they go for lunch. They decide to flip acoin until it lands showing heads. If the first flip shows heads, then Corey gets to choose. If heads shows onthe second flip or later, then Yin gets to choose.Is this a fair way […]<\/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-165357","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165357","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=165357"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/165357\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=165357"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=165357"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=165357"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}