{"id":238870,"date":"2025-06-18T12:52:11","date_gmt":"2025-06-18T12:52:11","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=238870"},"modified":"2025-06-18T12:52:14","modified_gmt":"2025-06-18T12:52:14","slug":"at-a-fabric-store-the-probability-that-a-customer-buys-thread-is-0-15","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/18\/at-a-fabric-store-the-probability-that-a-customer-buys-thread-is-0-15\/","title":{"rendered":"At a fabric store, the probability that a customer buys thread is 0.15."},"content":{"rendered":"\n<p>At a fabric store, the probability that a customer buys thread is 0.15. The probability that a customer buys a needle given that the customer buys thread is 0.25. Which statement is true? A. Buying a needle and buying a thread are independent events. B. Every customer who buys a thread also buys a needle. C. Buying a needle and buying a thread are dependent events. D. The probability that a customer buys a needle and thread is a 0.10.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer: C. Buying a needle and buying a thread are dependent events.<\/strong><\/p>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>In probability, two events are said to be <em>independent<\/em> if the occurrence of one event does not affect the probability of the other. In this case, we are given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The probability that a customer buys <strong>thread<\/strong> is <strong>P(Thread) = 0.15<\/strong><\/li>\n\n\n\n<li>The probability that a customer buys a <strong>needle given that they bought thread<\/strong> is <strong>P(Needle | Thread) = 0.25<\/strong><\/li>\n<\/ul>\n\n\n\n<p>To check whether the events are independent, compare the conditional probability <strong>P(Needle | Thread)<\/strong> with the unconditional probability <strong>P(Needle)<\/strong>. However, the value for <strong>P(Needle)<\/strong> alone is not given. Still, we can determine dependency by using the definition of dependent events.<\/p>\n\n\n\n<p>Two events <strong>A<\/strong> and <strong>B<\/strong> are dependent if <strong>P(B | A) \u2260 P(B)<\/strong>. In this scenario, <strong>P(Needle | Thread) = 0.25<\/strong>, and we cannot say this is equal to <strong>P(Needle)<\/strong> unless it is given or calculated.<\/p>\n\n\n\n<p>However, we can deduce something further. The fact that <strong>P(Needle | Thread) = 0.25<\/strong> is a conditional probability implies that the likelihood of buying a needle <strong>changes<\/strong> depending on whether the customer bought thread. That is the essence of dependence. If the events were independent, <strong>P(Needle | Thread)<\/strong> would equal <strong>P(Needle)<\/strong>.<\/p>\n\n\n\n<p>So the given information clearly shows that the probability of buying a needle is influenced by whether or not the customer buys thread. This is a classic example of dependent events.<\/p>\n\n\n\n<p>Let us also rule out the other options:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A<\/strong> is incorrect because the events are not independent.<\/li>\n\n\n\n<li><strong>B<\/strong> is incorrect because only 25 percent of thread buyers also buy needles, not all.<\/li>\n\n\n\n<li><strong>D<\/strong> is incorrect because <strong>P(Needle and Thread) = P(Thread) \u00d7 P(Needle | Thread) = 0.15 \u00d7 0.25 = 0.0375<\/strong>, not 0.10.<\/li>\n<\/ul>\n\n\n\n<p>Thus, the correct choice is <strong>C<\/strong> \u2014 the events are dependent.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1102.jpeg\" alt=\"\" class=\"wp-image-238871\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>At a fabric store, the probability that a customer buys thread is 0.15. The probability that a customer buys a needle given that the customer buys thread is 0.25. Which statement is true? A. Buying a needle and buying a thread are independent events. B. Every customer who buys a thread also buys a needle. [&hellip;]<\/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-238870","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238870","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=238870"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238870\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=238870"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=238870"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=238870"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}