{"id":287,"date":"2024-04-01T14:00:42","date_gmt":"2024-04-01T13:00:42","guid":{"rendered":"https:\/\/tutors4you.com\/?page_id=287"},"modified":"2024-04-01T14:00:43","modified_gmt":"2024-04-01T13:00:43","slug":"multiplication-theorem-on-probability","status":"publish","type":"page","link":"https:\/\/tutors4you.com\/index.php\/multiplication-theorem-on-probability\/","title":{"rendered":"Multiplication Theorem on Probability"},"content":{"rendered":"\n\n\t\t<div class=\"well well-sm\">\n\t\t\n\t\t<p>If A and B are the events associated with a random experiment then \n\t\t<\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/multiplicationprobability1.png\" class=\"img-responsive\">provided P(A)&ne; 0\n\t\t<\/br> and\n\t\t<\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/multiplicationprobability2.png\" class=\"img-responsive\"> provided P(B)&ne; 0<\/p>\n\t\t<\/div>\n\t\t\n\t\t<div class=\"well well-sm\">\n\t\t<h3>Extension of Multiplication Theorem<\/h3>\n\t\t<p>If A, B and C are three events associated with a random experiment, then\n\t\t<\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/multiplicationprobability3.png\" class=\"img-responsive\">\n\t\t<\/br> If A<sub>1<\/sub>, A<sub>2<\/sub>&#8230;.A<sub>n<\/sub> are associated with a random experiment, then\n\t\t<\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/multiplicationprobability4.png\" class=\"img-responsive\">\n\t\t<\/p>\n\t\t<\/div>\n\t\t\n\t\t<div class=\"well well-sm\">\n\t\t<h2>Independent Events<\/h2>\n\t\t<p>Two events are called independent if the occurrence or non-occurence of one does not affect the probability of the occurence\n\t\tof the other.\n\t\t<\/br><\/br>Two events A and B associated with a random experiment are independent if \n\t\t<\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/multiplicationprobability5.png\" class=\"img-responsive\">provided P(B)&ne; 0\n\t\t<\/br><\/br>and<img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/multiplicationprobability6.png\" class=\"img-responsive\">provided P(A)&ne; 0\n\t\t<\/br><\/br>Also \n\t\t<\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/multiplicationprobability7.png\" class=\"img-responsive\">\n\t\t<\/br><\/br> If  A<sub>1<\/sub>, A<sub>2<\/sub>&#8230;.A<sub>n<\/sub> associated with a random experiment are independent  then\n\t\t<\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/multiplicationprobability8.png\" class=\"img-responsive\">\n\t\t<\/p>\n\t\t<\/div>\n\t\t\n\t\t<div class=\"well well-sm\">\n\t\t<h3>Theorem<\/h3>\n\t\t<p>If A, B are independent events, then so are\n\t\t<\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/multiplicationprobability9.png\">or<img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/multiplicationprobability10.png\">\n\t\t<\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/multiplicationprobability11.png\">or<img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/multiplicationprobability12.png\">\n\t\t<\/br><\/br><img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/multiplicationprobability13.png\">or<img decoding=\"async\" src=\"\/wp-content\/uploads\/2024\/03\/multiplicationprobability14.png\">\n\t\t<\/p>\n\t\t<\/div>\n\t\n","protected":false},"excerpt":{"rendered":"<p>If A and B are the events associated with a random experiment then provided P(A)&ne; 0 and provided P(B)&ne; 0 Extension of Multiplication Theorem If A, B and C are three events associated with a random experiment, then If A1, A2&#8230;.An are associated with a random experiment, then Independent Events Two events are called independent [&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-287","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>Multiplication Theorem on 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\/multiplication-theorem-on-probability\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Multiplication Theorem on Probability - Tutors 4 You\" \/>\n<meta property=\"og:description\" content=\"If A and B are the events associated with a random experiment then provided P(A)&ne; 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