{"id":167512,"date":"2024-11-15T19:16:39","date_gmt":"2024-11-15T19:16:39","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=167512"},"modified":"2024-11-15T19:16:41","modified_gmt":"2024-11-15T19:16:41","slug":"imagine-i-flip-a-coin-100-times-in-a-sequence-and-you-need-to-guess-the-sequence","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/15\/imagine-i-flip-a-coin-100-times-in-a-sequence-and-you-need-to-guess-the-sequence\/","title":{"rendered":"Imagine I flip a coin 100 times in a sequence, and you need to guess the sequence."},"content":{"rendered":"\n

Imagine I flip a coin 100 times in a sequence, and you need to guess the sequence. You are allowed to ask one yes\/no question. What do you ask to maximize the probability of guessing the correct sequence<\/p>\n\n\n\n

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

To maximize the probability of guessing the correct sequence of 100 coin flips, the most effective yes\/no question to ask would be:<\/p>\n\n\n\n

“Is the sequence of coin flips symmetrical?”<\/strong><\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

The core idea behind this strategy is to leverage the structural properties of the sequence rather than attempting to guess each individual flip. Let\u2019s break it down step by step:<\/p>\n\n\n\n

    \n
  1. Symmetry of Sequences:<\/strong><\/li>\n<\/ol>\n\n\n\n
      \n
    • A sequence is said to be symmetrical<\/strong> if it reads the same forward and backward (like a palindrome). For example, “HTTHT” is symmetrical, but “HTTHH” is not.<\/li>\n\n\n\n
    • The question directly probes the overall structure of the sequence. If the answer is “yes”<\/strong>, it means the sequence has a symmetry that can be exploited. If the answer is “no”<\/strong>, the sequence has no such symmetry, and you know you are dealing with a non-symmetric configuration.<\/li>\n<\/ul>\n\n\n\n
        \n
      1. Probabilistic Advantage:<\/strong><\/li>\n<\/ol>\n\n\n\n
          \n
        • If the sequence is symmetrical, the number of possible sequences reduces significantly. For instance, in a sequence of 100 flips, knowing that the sequence is symmetrical means you only need to guess half of the sequence, and the rest is automatically determined. For a 100-flip sequence, this halves the number of possibilities.<\/li>\n\n\n\n
        • If the answer is “no”, the sequence is non-symmetric, but by understanding this, you still eliminate half of the possible configurations, simplifying your task to guessing the exact arrangement from the remaining possibilities.<\/li>\n<\/ul>\n\n\n\n
            \n
          1. Maximizing the Guessing Probability:<\/strong><\/li>\n<\/ol>\n\n\n\n
              \n
            • By asking if the sequence is symmetrical, you cut the total number of possible outcomes in half. Since there are (2^{100}) possible sequences, the symmetry question effectively reduces the space of possible answers from (2^{100}) to (2^{99}), significantly increasing your chances of guessing the sequence correctly. Even though you still need to make the correct guess, the total set of possibilities has been narrowed down considerably.<\/li>\n<\/ul>\n\n\n\n

              In conclusion, asking whether the sequence is symmetrical is a strategic question that maximizes the probability of correctly guessing the sequence of coin flips, utilizing the structural property of symmetry to reduce the number of possibilities.<\/p>\n","protected":false},"excerpt":{"rendered":"

              Imagine I flip a coin 100 times in a sequence, and you need to guess the sequence. You are allowed to ask one yes\/no question. What do you ask to maximize the probability of guessing the correct sequence The Correct Answer and Explanation is: To maximize the probability of guessing the correct sequence of 100 […]<\/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-167512","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167512","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=167512"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167512\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167512"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167512"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167512"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}