{"id":238862,"date":"2025-06-18T12:47:36","date_gmt":"2025-06-18T12:47:36","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=238862"},"modified":"2025-06-18T12:47:38","modified_gmt":"2025-06-18T12:47:38","slug":"a-marketing-firm-tracks-data-on-grocery-store-visits-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/18\/a-marketing-firm-tracks-data-on-grocery-store-visits-2\/","title":{"rendered":"A marketing firm tracks data on grocery store visits."},"content":{"rendered":"\n<pre id=\"preorder-ask-header-text\" class=\"wp-block-preformatted\">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 _____ 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<\/pre>\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, consider the definition of independence in probability. Two events, A and B, are said to be independent if the occurrence of one does not affect the probability of the other occurring. Mathematically, this means that:<\/p>\n\n\n\n<p><strong>P(A and B) = P(A) \u00d7 P(B)<\/strong><\/p>\n\n\n\n<p>In this problem, the marketing firm provides the following data:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Probability that a shopper buys bread, P(A) = 0.60<\/li>\n\n\n\n<li>Probability that a shopper buys cheese, P(B) = 0.20<\/li>\n<\/ul>\n\n\n\n<p>If these two events are independent, the probability that a shopper buys both bread and cheese would be:<\/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>Thus, the condition for A and B to be independent is that the probability of both occurring together equals 0.12. This matches option C, making it the correct choice.<\/p>\n\n\n\n<p>Let\u2019s briefly consider why the other options are incorrect:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Option A: the probability of buying bread or cheese is 0.12<\/strong>. This is incorrect. The formula for the probability of A or B is <strong>P(A or B) = P(A) + P(B) \u2013 P(A and B)<\/strong>. Using the given data and assuming independence, this becomes <strong>0.60 + 0.20 \u2013 0.12 = 0.68<\/strong>, not 0.12.<\/li>\n\n\n\n<li><strong>Option B: the probability of buying bread and cheese is 0<\/strong>. This would mean the events are mutually exclusive, not independent.<\/li>\n\n\n\n<li><strong>Option D: the probability of buying bread or cheese is 0.80<\/strong>. That would imply <strong>P(A and B) = 0.60 + 0.20 \u2013 0.80 = 0.00<\/strong>, which contradicts the expected value of 0.12 under independence.<\/li>\n<\/ul>\n\n\n\n<p>Therefore, the correct and logically supported answer is <strong>C<\/strong>.<\/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-banner8-1100.jpeg\" alt=\"\" class=\"wp-image-238863\"\/><\/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-238862","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238862","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=238862"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/238862\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=238862"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=238862"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=238862"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}