{"id":205862,"date":"2025-03-25T18:50:25","date_gmt":"2025-03-25T18:50:25","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=205862"},"modified":"2025-03-25T18:50:27","modified_gmt":"2025-03-25T18:50:27","slug":"which-of-the-following-are-binomial-experiments","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/25\/which-of-the-following-are-binomial-experiments\/","title":{"rendered":"Which of the following are binomial experiments"},"content":{"rendered":"\n

Which of the following are binomial experiments? For those are not, indicate which part of the definition of binomial experiment does not apply.<\/p>\n\n\n\n

Tossing a fair coin 1000 times and counting the number of times a head appears.
Tossing a fair coin and counting the number of tosses before a head appears.
Checking five students for drug use from a class of thirty students in which ten percent use drugs.<\/p>\n\n\n\n

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

Answer:<\/h3>\n\n\n\n
    \n
  1. Tossing a fair coin 1000 times and counting the number of times a head appears<\/strong><\/li>\n<\/ol>\n\n\n\n
      \n
    • This is a binomial experiment<\/strong> because it satisfies all four conditions of a binomial experiment:\n
        \n
      • Fixed number of trials (1000 tosses<\/strong>).<\/li>\n\n\n\n
      • Two possible outcomes per trial (Head or Tail<\/strong>).<\/li>\n\n\n\n
      • The probability of success (getting heads<\/strong>) is constant at 0.5.<\/li>\n\n\n\n
      • The trials are independent.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
          \n
        1. Tossing a fair coin and counting the number of tosses before a head appears<\/strong><\/li>\n<\/ol>\n\n\n\n
            \n
          • This is not<\/strong> a binomial experiment because it does not have a fixed number of trials<\/strong>. Instead, the number of trials is random, stopping only when a head appears. This is actually a geometric experiment<\/strong> rather than a binomial one.<\/li>\n<\/ul>\n\n\n\n
              \n
            1. Checking five students for drug use from a class of thirty students in which ten percent use drugs<\/strong><\/li>\n<\/ol>\n\n\n\n
                \n
              • This is not strictly a binomial experiment<\/strong> because the probability of selecting a drug user changes after each selection<\/strong> (since students are not replaced). This violates the assumption of independent trials with constant probability<\/strong>. However, if the sample size were much smaller compared to the population, we could approximate it as binomial.<\/li>\n<\/ul>\n\n\n\n
                \n\n\n\n

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

                A binomial experiment<\/strong> must satisfy four conditions:<\/p>\n\n\n\n

                  \n
                1. Fixed number of trials (n)<\/strong>: The experiment must have a predetermined number of trials.<\/li>\n\n\n\n
                2. Only two possible outcomes per trial<\/strong>: Each trial results in either a success or a failure.<\/li>\n\n\n\n
                3. Constant probability of success (p)<\/strong>: The probability of success must remain the same for each trial.<\/li>\n\n\n\n
                4. Independence<\/strong>: The outcome of one trial must not affect the outcome of another.<\/li>\n<\/ol>\n\n\n\n

                  The first experiment<\/strong> (1000 coin tosses) meets all conditions, making it binomial.
                  The second experiment<\/strong> (counting tosses until first head) lacks a fixed number of trials, making it geometric instead.
                  The third experiment<\/strong> (student drug testing) lacks independence because the probability of selecting a drug user changes after each selection, making it a hypergeometric experiment<\/strong> rather than binomial.<\/p>\n\n\n\n

                  \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

                  Which of the following are binomial experiments? For those are not, indicate which part of the definition of binomial experiment does not apply. Tossing a fair coin 1000 times and counting the number of times a head appears.Tossing a fair coin and counting the number of tosses before a head appears.Checking five students for drug […]<\/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-205862","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/205862","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=205862"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/205862\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=205862"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=205862"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=205862"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}