{"id":240,"date":"2025-05-07T10:36:00","date_gmt":"2025-05-07T10:36:00","guid":{"rendered":"https:\/\/yaveni.com\/blog\/?p=240"},"modified":"2025-05-07T10:36:01","modified_gmt":"2025-05-07T10:36:01","slug":"a-grocer-noticed-that-customers-buy-both-pet-and-baby-supplies-with-a-probability-of-0-12","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-grocer-noticed-that-customers-buy-both-pet-and-baby-supplies-with-a-probability-of-0-12\/","title":{"rendered":"A grocer noticed that customers buy both pet and baby supplies with a probability of 0.12"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">A grocer noticed that customers buy both pet and baby supplies with a probability of 0.12 . Considered separately, the probability that a customer buys pet supplies is P(A)=0.64, and the probability that a customer buys baby supplies is P(B)=0.25.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To solve this problem, we need to use the formula for the probability of the union of two events, A (buying pet supplies) and B (buying baby supplies). The problem provides the following probabilities:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$P(A) = 0.64$ (the probability that a customer buys pet supplies)<\/li>\n\n\n\n<li>$P(B) = 0.25$ (the probability that a customer buys baby supplies)<\/li>\n\n\n\n<li>$P(A \\cap B) = 0.12$ (the probability that a customer buys both pet and baby supplies)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">We are asked to find the probability that a customer buys either pet supplies, baby supplies, or both. This can be expressed as the union of the two events:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>P(A \\cup B) = P(A) + P(B) &#8211; P(A \\cap B)<br>$$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation of the Formula:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The formula above comes from the principle of inclusion-exclusion in probability theory. Here&#8217;s a breakdown:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$P(A \\cup B)$ is the probability that at least one of the two events happens (i.e., a customer buys either pet supplies, baby supplies, or both).<\/li>\n\n\n\n<li>$P(A)$ is the probability of buying pet supplies.<\/li>\n\n\n\n<li>$P(B)$ is the probability of buying baby supplies.<\/li>\n\n\n\n<li>$P(A \\cap B)$ is the probability of buying both pet and baby supplies.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">If we simply added $P(A)$ and $P(B)$, we would be double-counting the cases where customers buy both pet and baby supplies, so we subtract $P(A \\cap B)$ to correct for this.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Calculation:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>P(A \\cup B) = P(A) + P(B) &#8211; P(A \\cap B)<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>P(A \\cup B) = 0.64 + 0.25 &#8211; 0.12<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>P(A \\cup B) = 0.77<br>$$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The probability that a customer buys either pet supplies, baby supplies, or both is $0.77$, or 77%. This means there is a 77% chance that a customer will buy at least one of these items.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This calculation uses the principle of inclusion-exclusion, ensuring that we don&#8217;t double-count customers who purchase both pet and baby supplies. The result tells us that a substantial portion of customers buys either one or both types of products.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A grocer noticed that customers buy both pet and baby supplies with a probability of 0.12 . Considered separately, the probability that a customer buys pet supplies is P(A)=0.64, and the probability that a customer buys baby supplies is P(B)=0.25. The correct answer and explanation is : To solve this problem, we need to use [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-240","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/240","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=240"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/240\/revisions"}],"predecessor-version":[{"id":241,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/240\/revisions\/241"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=240"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=240"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}