{"id":285,"date":"2024-04-01T13:59:47","date_gmt":"2024-04-01T12:59:47","guid":{"rendered":"https:\/\/tutors4you.com\/?page_id=285"},"modified":"2024-04-01T13:59:48","modified_gmt":"2024-04-01T12:59:48","slug":"conditional-probability","status":"publish","type":"page","link":"https:\/\/tutors4you.com\/index.php\/conditional-probability\/","title":{"rendered":"Conditional Probability"},"content":{"rendered":"\n\n\t\t
\n\t\t\n\t\t

If A and B are two envents associated with a random experiment, then the probability of occurence of the event A\n\t\tunder the condition that B has occurred and P(B)≠0<\/p>\n\t\t

Thus P(A\/B)=probability of occurence of event A given that event B has already occured and P(B)≠0<\/p>\n\t\t

Let S be the sample space having ‘n’ equal likely outcomes of a random experiment. Let A and B be two events of sample space \n\t\tS.<\/p>\n\t\t

<\/br> a is number of outcomes in A\n\t\t<\/br>b is number of outcomes in B\n\t\t<\/br>t is number of outcomes in A∩B\n\t\t

<\/br>Then \n\t\t<\/br><\/br>        \n\t\t<\/p>\n\t\t

Note: The outcomes of B which are favourable to A are the common outcomes of A and B that is, outcomes of A&capB\n\t\t<\/p>\n\t\t

<\/br><\/br><\/p>\n\t\t

<\/br><\/br>provided P(B)≠0<\/p>\n\t\t

<\/br><\/br>orprovided P(B)≠0<\/p>\n\t\t

<\/br><\/br>Similarlyprovided P(A)≠0<\/p>\n\t\t\n\t\t<\/div>\n\t\t\n\t\t

\n\t\t

Properties of Conditional Probability<\/h3>\n\t\t

The conditional probability of an event A given that B has occurred lies between 0 and 1<\/p>\n\t\t

<\/br>If A and B are two events associated with a random experiment having sample space S and if F \n\t\tis an event such that P(F)≠0, then \n\t\t<\/br><\/br>\n\t\t<\/br>and if A and B are disjoint sets\n\t\t<\/br><\/br>\n\t\t<\/p>\n\t\t

<\/br><\/br>\n\t\t<\/p>\n\t\t\n\t\t<\/div>\n\t\t\n\t\t\n\t\n","protected":false},"excerpt":{"rendered":"

If A and B are two envents associated with a random experiment, then the probability of occurence of the event A under the condition that B has occurred and P(B)≠0 Thus P(A\/B)=probability of occurence of event A given that event B has already occured and P(B)≠0 Let S be the sample space having ‘n’ equal […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-285","page","type-page","status-publish","hentry"],"blocksy_meta":[],"yoast_head":"\nConditional Probability - Tutors 4 You<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/tutors4you.com\/index.php\/conditional-probability\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Conditional Probability - 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