{"id":283,"date":"2024-04-01T13:58:32","date_gmt":"2024-04-01T12:58:32","guid":{"rendered":"https:\/\/tutors4you.com\/?page_id=283"},"modified":"2024-04-01T13:58:33","modified_gmt":"2024-04-01T12:58:33","slug":"laws-of-probability","status":"publish","type":"page","link":"https:\/\/tutors4you.com\/index.php\/laws-of-probability\/","title":{"rendered":"Laws of Probability"},"content":{"rendered":"\n\n\t\t<div class=\"well well-sm\">\n\t\t<h3>Theorem 1<\/h3>\n\t\t<p>If A and B are events associated with a random experiment having sample space S and if <img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/\n\t\tAsubsetB.png\" class = \"img-responsive\">, then\n\t\t<\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/P(A)lessthanequalP(B).png\" class=\"img-responsive\">\n\t\t<\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/Theorem1B.png\" class=\"img-responsive\"><\/p>\n\t\tIf A and B are mutually exclusive events associated with a random experiment having sample space S, then\n\t\t<\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/mutuallyexclusive.png\" class=\"img-responsive\">\n\t\tIf <img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/A1toAn.png\">are mutually exclusive events associated with a random experiment, then\n\t\t<\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/mutuallyexclusive2.png\" class=\"img-responsive\"><\/p>\n\t\t<\/div>\n\t\t\n\t\t<div class=\"well well-sm\">\n\t\t<h3>Theorem 2<\/h3>\n\t\t<p>If A and B are mutually exclusive and exhausive events associated with a random experiment having sample space S, then\n\t\t<\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/theorem2A.png\" class=\"img-responsive\"><\/p>\n\t\t<\/br><\/br> If <img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/A1toAn.png\"> are mutually exclusive and exhaustive events associated with\n\t\trandom experiment having sample space S, then \n\t\t<\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/theorem2B.png\" class=\"img-responsive\"><\/p>\n\t\t<\/p>\n\t\t<\/div>\n\t\t\n\t\t<div class=\"well well-sm\">\n\t\t<h3>Theorem 3<\/h3>\n\t\t<p>If A and B are any two events associated with a random experiment having sample space S, then\n\t\t<\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/theorem3.png\" class=\"img-responsive\"><\/p>\n\t\t<\/p>\n\t\t<\/div>\n\t\t\n\t\t<div class=\"well well-sm\">\n\t\t<h3>Theorem 4<\/h3>\n\t\t<p>If A and B are any two events associated with a random experiment, then<\/P>\n\t\t<p><\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/Theorem4A.png\" class=\"img-responsive\"><\/p>\n\t\t<p><\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/Theorem4B.png\" class=\"img-responsive\"><\/p>\n\t\t<p><\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/Theorem4C.png\" class=\"img-responsive\"><\/p>\n\t\t<p><\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/Theorem4D.png\" class=\"img-responsive\"><\/p>\n\t\t<p><\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/Theorem4E.png\" class=\"img-responsive\">Probability of occurence of A only<\/p>\n\t\t<p><\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/Theorem4F.png\" class=\"img-responsive\">Probability of occurence of B only<\/p>\n\t\t<p><\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/Theorem4G.png\" class=\"img-responsive\"><\/p>\n\t\t<p><\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/Theorem4H.png\" class=\"img-responsive\"> is the probability of occurence\n\t\tof only (or exactly) one of the two events A and B.<\/p>\n\t\t<\/div>\n\t\t\n\t\t<div class=\"well well-sm\">\n\t\t<h3>Theorem 5<\/h3>\n\t\t<p>If A, B and C are any three events associated with a random experiment, then\n\t\t<\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/Theorem5.png\" class=\"img-responsive\"><\/p>\n\t\t<\/div>\n\t\t\n\t\t<div class=\"well well-sm\">\n\t\t<h3>Other Important Properties<\/h3>\n\t\t<p><\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/otherproperties1.png\" class=\"img-responsive\">\n\t\t<\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/otherproperties2.png\" class=\"img-responsive\"><\/p>\n\t\t<p><\/br><\/br>If odds in favour of an event A are a:b then \n\t\t<\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/otherproperties3.png\" class=\"img-responsive\">\n\t\t<\/br><\/br>If odds against an event A are a:b then \n\t\t<\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/otherproperties4.png\" class=\"img-responsive\">\n\t\t<\/br><\/br>If probability of an event is p then odds in favour are\n\t\t<\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/otherproperties5.png\" class=\"img-responsive\">\n\t\t\n\t\t<\/p>\n\t\t\n\t\t\n\t\t<\/div>\n\t\t\n\t\n","protected":false},"excerpt":{"rendered":"<p>Theorem 1 If A and B are events associated with a random experiment having sample space S and if , then If A and B are mutually exclusive events associated with a random experiment having sample space S, then If are mutually exclusive events associated with a random experiment, then Theorem 2 If A and [&hellip;]<\/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-283","page","type-page","status-publish","hentry"],"blocksy_meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Laws of Probability - Tutors 4 You<\/title>\n<meta name=\"robots\" content=\"index, follow, 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