{"id":156264,"date":"2022-03-26T01:33:50","date_gmt":"2022-03-25T20:03:50","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/conditional-probability-and-its-examples\/"},"modified":"2022-12-22T21:37:50","modified_gmt":"2022-12-22T16:07:50","slug":"conditional-probability-and-its-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/","title":{"rendered":"Conditional Probability and It&#8217;s Examples"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/#Conditional_Probability\" title=\"Conditional Probability\">Conditional Probability<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/#Conditional_Probability_Definition\" title=\"Conditional Probability Definition:\">Conditional Probability Definition:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/#Conditional_Probability_Examples\" title=\"Conditional Probability Examples:\">Conditional Probability Examples:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/#Conditional_Probability_Formula\" title=\"Conditional Probability Formula:\">Conditional Probability Formula:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/#Conditional_Property_Problems\" title=\"Conditional Property Problems:\">Conditional Property Problems:<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Conditional_Probability\"><\/span>Conditional Probability<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Conditional Probability is a measure of the likelihood of an event occurring, given that another event has occurred. In other words, it is a way of quantifying the relationship between two events.<\/p>\n<p>For example, let&#8217;s say that you are rolling a die. The probability of getting a six is 1\/6, regardless of what has happened previously. However, if you are told that a six has already been rolled, the probability of getting another six is now 2\/6, because the first six has already occurred.<\/p>\n<p>In general, the conditional <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/probability\/\" target=\"_blank\" rel=\"noopener\">probability<\/a> of an event A, given that event B has occurred, is written as P(A|B) and is calculated as follows:<\/p>\n<p>P(A|B) = P(A and B) \/ P(B)<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156263 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/conditional-probability-and-its-examples.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/conditional-probability-and-its-examples.jpg?v=1648238627 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/conditional-probability-and-its-examples-300x212.jpg?v=1648238627 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Conditional_Probability_Definition\"><\/span>Conditional Probability Definition:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The conditional probability of an event A happening given that another event B has already happened is given by:<\/p>\n<p>P(A|B) = P(A and B) \/ P(B)<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Conditional_Probability_Examples\"><\/span>Conditional Probability Examples:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. A die is rolled. What is the probability of getting a 3?<\/p>\n<p>The probability of getting a 3 is 1\/6.<\/p>\n<p>2. A coin is flipped. What is the probability of getting a heads?<\/p>\n<p>The probability of getting a heads is 1\/2.<\/p>\n<p>3. A card is drawn from a deck of cards. What is the probability of getting a club?<\/p>\n<p>The probability of getting a club is 1\/4.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Conditional_Probability_Formula\"><\/span>Conditional Probability Formula:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The conditional probability formula is a mathematical equation that calculates the probability of an event occurring, given that another event has already occurred. The formula is written as: P(A|B) = P(A and B)\/P(B). The first term, P(A|B), is the probability of event A occurring, given that event B has already occurred. The second term, P(A and B), is the probability of both events A and B occurring. The third term, P(B), is the probability of event B occurring, independent of event A.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Conditional_Property_Problems\"><\/span>Conditional Property Problems:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. The conditional statement is always false.<\/p>\n<p>2. The conditional statement is always true.<\/p>\n<p>3. The truth of the conditional statement depends on the truth of the antecedent.<\/p>\n<p>4. The truth of the conditional statement depends on the truth of the consequent.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Conditional Probability Conditional Probability is a measure of the likelihood of an event occurring, given that another event has occurred. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Conditional Probability and It's Examples","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Conditional Probability and It's Examples in Maths topic of Maths in details explained by subject experts on infinitylearn.com. Register free for online tutoring session to clear your doubts.","custom_permalink":"maths\/conditional-probability-and-its-examples\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Conditional Probability and It&#039;s Examples - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about Conditional Probability and It&#039;s Examples in Maths topic of Maths in details explained by subject experts on infinitylearn.com. Register free for online tutoring session to clear your doubts.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Conditional Probability and It&#039;s Examples - Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"og:description\" content=\"Learn about Conditional Probability and It&#039;s Examples in Maths topic of Maths in details explained by subject experts on infinitylearn.com. Register free for online tutoring session to clear your doubts.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:published_time\" content=\"2022-03-25T20:03:50+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-12-22T16:07:50+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/conditional-probability-and-its-examples.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"vipin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Conditional Probability and It's Examples - Infinity Learn by Sri Chaitanya","description":"Learn about Conditional Probability and It's Examples in Maths topic of Maths in details explained by subject experts on infinitylearn.com. Register free for online tutoring session to clear your doubts.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/","og_locale":"en_US","og_type":"article","og_title":"Conditional Probability and It's Examples - Infinity Learn by Sri Chaitanya","og_description":"Learn about Conditional Probability and It's Examples in Maths topic of Maths in details explained by subject experts on infinitylearn.com. Register free for online tutoring session to clear your doubts.","og_url":"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_published_time":"2022-03-25T20:03:50+00:00","article_modified_time":"2022-12-22T16:07:50+00:00","og_image":[{"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/conditional-probability-and-its-examples.jpg"}],"twitter_card":"summary_large_image","twitter_creator":"@InfinityLearn_","twitter_site":"@InfinityLearn_","twitter_misc":{"Written by":"vipin","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/#primaryimage","inLanguage":"en-US","url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/conditional-probability-and-its-examples.jpg?v=1648238627","contentUrl":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/conditional-probability-and-its-examples.jpg?v=1648238627","width":606,"height":428},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/","name":"Conditional Probability and It's Examples - Infinity Learn by Sri Chaitanya","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"primaryImageOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/#primaryimage"},"datePublished":"2022-03-25T20:03:50+00:00","dateModified":"2022-12-22T16:07:50+00:00","description":"Learn about Conditional Probability and It's Examples in Maths topic of Maths in details explained by subject experts on infinitylearn.com. Register free for online tutoring session to clear your doubts.","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"Conditional Probability and It&#8217;s Examples"}]},{"@type":"Article","@id":"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/#article","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/#webpage"},"author":{"@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/d931698bc4645b2739855720864f30e2"},"headline":"Conditional Probability and It&#8217;s Examples","datePublished":"2022-03-25T20:03:50+00:00","dateModified":"2022-12-22T16:07:50+00:00","mainEntityOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/#webpage"},"wordCount":352,"publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/maths\/conditional-probability-and-its-examples\/#primaryimage"},"thumbnailUrl":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/conditional-probability-and-its-examples.jpg","articleSection":["Maths"],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/d931698bc4645b2739855720864f30e2","name":"vipin","image":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/c9a84adf9d11e7ad01332089c3e52538?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/c9a84adf9d11e7ad01332089c3e52538?s=96&d=mm&r=g","caption":"vipin"},"sameAs":["http:\/\/surge.infinitylearn.com"],"url":"https:\/\/infinitylearn.com\/surge\/author\/vipin\/"}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/156264"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/comments?post=156264"}],"version-history":[{"count":0,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/156264\/revisions"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=156264"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=156264"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/tags?post=156264"},{"taxonomy":"table_tags","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/table_tags?post=156264"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}