{"id":202251,"date":"2025-03-17T09:52:38","date_gmt":"2025-03-17T09:52:38","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=202251"},"modified":"2025-03-17T09:52:40","modified_gmt":"2025-03-17T09:52:40","slug":"the-probability-of-event-a-occurring-is-0-3-while-the-probability-that-event-b-occurs-is-0-8","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/17\/the-probability-of-event-a-occurring-is-0-3-while-the-probability-that-event-b-occurs-is-0-8\/","title":{"rendered":"The probability of event A occurring is 0.3, while the probability that event B occurs is 0.8"},"content":{"rendered":"\n<p>The probability of event A occurring is 0.3, while the probability that event B occurs is 0.8. The probability that event A and event B occur simultaneously is 0.2. If it is known that event A occurred, what is the probability that event B occurred also?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To solve this problem, we need to calculate the conditional probability that event B occurs given that event A has already occurred. This is represented mathematically as P(B\u2223A)P(B | A), which is the probability of event B occurring given that event A has occurred.<\/p>\n\n\n\n<p>The formula for conditional probability is: P(B\u2223A)=P(A\u2229B)P(A)P(B | A) = \\frac{P(A \\cap B)}{P(A)}<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P(A\u2229B)P(A \\cap B) is the probability that both event A and event B occur simultaneously.<\/li>\n\n\n\n<li>P(A)P(A) is the probability that event A occurs.<\/li>\n<\/ul>\n\n\n\n<p>From the problem, we are given the following values:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>P(A)=0.3P(A) = 0.3<\/li>\n\n\n\n<li>P(B)=0.8P(B) = 0.8<\/li>\n\n\n\n<li>P(A\u2229B)=0.2P(A \\cap B) = 0.2<\/li>\n<\/ul>\n\n\n\n<p>We are asked to find P(B\u2223A)P(B | A), the probability of event B occurring given that event A has occurred. Plugging the known values into the formula: P(B\u2223A)=P(A\u2229B)P(A)=0.20.3P(B | A) = \\frac{P(A \\cap B)}{P(A)} = \\frac{0.2}{0.3} P(B\u2223A)=23\u22480.6667P(B | A) = \\frac{2}{3} \\approx 0.6667<\/p>\n\n\n\n<p>Thus, the probability that event B occurs given that event A has occurred is approximately <strong>0.6667<\/strong> or <strong>66.67%<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>Conditional probability describes the likelihood of an event occurring given that another event has already occurred. In this case, we are given the probability of event A occurring, the probability of both events A and B occurring together, and the probability of event B occurring independently. Using these values, we apply the conditional probability formula to find how the occurrence of event A affects the likelihood of event B happening. The result tells us that when we know event A has occurred, there is a 66.67% chance that event B will also occur.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The probability of event A occurring is 0.3, while the probability that event B occurs is 0.8. The probability that event A and event B occur simultaneously is 0.2. If it is known that event A occurred, what is the probability that event B occurred also? The correct answer and explanation is : To solve [&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-202251","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/202251","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=202251"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/202251\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=202251"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=202251"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=202251"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}