{"id":238866,"date":"2025-06-18T12:49:56","date_gmt":"2025-06-18T12:49:56","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=238866"},"modified":"2025-06-18T12:49:58","modified_gmt":"2025-06-18T12:49:58","slug":"a-marketing-firm-tracks-data-on-grocery-store-visits-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/18\/a-marketing-firm-tracks-data-on-grocery-store-visits-3\/","title":{"rendered":"A marketing firm tracks data on grocery store visits"},"content":{"rendered":"\n<p>A marketing firm tracks data on grocery store visits. In one study, it finds that the probability that a shopper buys bread during a visit to the grocery store is 0.60, and the probability that a shopper buys cheese is 0.20. Event A = A shopper buys bread. Event B = A shopper buys cheese. A and B are independent events if <strong>_<\/strong> A. the probability of buying bread or cheese is 0.12 B. the probability of buying bread and cheese is 0 C. the probability of buying bread and cheese is 0.12 D. the probability of buying bread or cheese is 0.80 SUBMIT<\/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. the probability of buying bread and cheese is 0.12<\/strong><\/p>\n\n\n\n<p>To determine whether two events are independent, use the <strong>definition of independence<\/strong>:<br>Two events A and B are independent <strong>if and only if<\/strong><br><strong>P(A and B) = P(A) \u00d7 P(B)<\/strong><\/p>\n\n\n\n<p>In this problem:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P(A) = probability that a shopper buys bread = 0.60<\/li>\n\n\n\n<li>P(B) = probability that a shopper buys cheese = 0.20<\/li>\n<\/ul>\n\n\n\n<p>If events A and B are independent, then:<\/p>\n\n\n\n<p><strong>P(A and B) = 0.60 \u00d7 0.20 = 0.12<\/strong><\/p>\n\n\n\n<p>So, if the <strong>probability that a shopper buys both bread and cheese is 0.12<\/strong>, then the events are independent. This is exactly what option C states.<\/p>\n\n\n\n<p>Now, look at the other options:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Option A: \u201cThe probability of buying bread or cheese is 0.12\u201d is incorrect. The probability of A or B is calculated by<br><strong>P(A or B) = P(A) + P(B) \u2212 P(A and B)<\/strong><br>If A and B are independent, then P(A or B) = 0.60 + 0.20 \u2212 0.12 = 0.68. So, 0.12 is not correct.<\/li>\n\n\n\n<li>Option B: \u201cThe probability of buying bread and cheese is 0\u201d would imply that it is impossible to buy both at the same time. This would make A and B <strong>mutually exclusive<\/strong>, not independent.<\/li>\n\n\n\n<li>Option D: \u201cThe probability of buying bread or cheese is 0.80\u201d is also incorrect. As shown, P(A or B) equals 0.68, <strong>not<\/strong> 0.80, under the independence assumption.<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the only correct condition for independence is when the <strong>joint probability equals the product of the individual probabilities<\/strong>, which makes <strong>option C<\/strong> the best choice.<\/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-banner8-1101.jpeg\" alt=\"\" class=\"wp-image-238867\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>A marketing firm tracks data on grocery store visits. In one study, it finds that the probability that a shopper buys bread during a visit to the grocery store is 0.60, and the probability that a shopper buys cheese is 0.20. Event A = A shopper buys bread. Event B = A shopper buys cheese. [&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-238866","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238866","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=238866"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238866\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=238866"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=238866"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=238866"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}