{"id":230039,"date":"2025-06-08T18:51:15","date_gmt":"2025-06-08T18:51:15","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=230039"},"modified":"2025-06-08T18:51:18","modified_gmt":"2025-06-08T18:51:18","slug":"becky-has-30-t-shirts-in-a-drawer-12-concert-shirts-8-team-shirts-and-10-plain-shirts","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/08\/becky-has-30-t-shirts-in-a-drawer-12-concert-shirts-8-team-shirts-and-10-plain-shirts\/","title":{"rendered":"Becky has 30 t-shirts in a drawer: 12 concert shirts, 8 team shirts, and 10 plain shirts"},"content":{"rendered":"\n

Becky has 30 t-shirts in a drawer: 12 concert shirts, 8 team shirts, and 10 plain shirts. Of the 10 shirts she randomly selects to give to charity, 3 are concert shirts. How does this frequency compare to the expected frequency based on the probability of randomly selecting a concert shirt? A. The frequency is 1 fewer than expected. B. The frequency is 9 fewer than expected. C. The frequency is 2 more than expected. D. The frequency is the same as expected.<\/p>\n\n\n\n

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

Correct Answer: A. The frequency is 1 fewer than expected.<\/strong><\/p>\n\n\n\n

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

Becky has a total of 30 t-shirts, divided into three categories:<\/p>\n\n\n\n

    \n
  • 12 concert shirts<\/li>\n\n\n\n
  • 8 team shirts<\/li>\n\n\n\n
  • 10 plain shirts<\/li>\n<\/ul>\n\n\n\n

    She randomly selects 10 shirts<\/strong> to give to charity, and 3<\/strong> of those happen to be concert shirts. The question asks how this observed frequency (3 concert shirts) compares to the expected frequency<\/strong> if the selection were purely random.<\/p>\n\n\n\n

    \n\n\n\n

    Step 1: Determine the Probability of Selecting a Concert Shirt<\/h3>\n\n\n\n

    The probability of randomly selecting a concert shirt from the drawer is:P(concert shirt)=1230=25P(\\text{concert shirt}) = \\frac{12}{30} = \\frac{2}{5}P(concert shirt)=3012\u200b=52\u200b<\/p>\n\n\n\n

    \n\n\n\n

    Step 2: Use the Probability to Find the Expected Frequency<\/h3>\n\n\n\n

    If Becky selects 10 shirts at random, and the probability of selecting a concert shirt is 25\\frac{2}{5}52\u200b, then the expected number<\/strong> of concert shirts is:Expected frequency=10\u00d725=4\\text{Expected frequency} = 10 \\times \\frac{2}{5} = 4Expected frequency=10\u00d752\u200b=4<\/p>\n\n\n\n

    \n\n\n\n

    Step 3: Compare the Expected and Actual Frequencies<\/h3>\n\n\n\n
      \n
    • Expected number of concert shirts: 4<\/strong><\/li>\n\n\n\n
    • Actual number of concert shirts selected: 3<\/strong><\/li>\n<\/ul>\n\n\n\n

      So, the actual frequency is 1 fewer<\/strong> than expected.<\/p>\n\n\n\n

      \n\n\n\n

      Conclusion:<\/h3>\n\n\n\n

      Although Becky selected her shirts randomly, randomness can lead to slight differences from expected outcomes. In this case, she ended up with 1 fewer concert shirt<\/strong> than what probability predicts on average. This slight variation is common in probability and statistics and does not imply any error or bias in the selection process. The correct comparison shows that the actual number is slightly lower than expected.<\/p>\n\n\n\n

      Therefore, the correct answer is: A. The frequency is 1 fewer than expected.<\/strong><\/p>\n\n\n\n

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

      Becky has 30 t-shirts in a drawer: 12 concert shirts, 8 team shirts, and 10 plain shirts. Of the 10 shirts she randomly selects to give to charity, 3 are concert shirts. How does this frequency compare to the expected frequency based on the probability of randomly selecting a concert shirt? A. The frequency is […]<\/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-230039","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230039","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=230039"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/230039\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=230039"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=230039"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=230039"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}