{"id":6045,"date":"2025-08-19T11:56:16","date_gmt":"2025-08-19T06:26:16","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=6045"},"modified":"2025-08-19T11:56:16","modified_gmt":"2025-08-19T06:26:16","slug":"axioms-of-probability","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ee\/probability-and-statistics\/axioms-of-probability","title":{"rendered":"Axioms of Probability"},"content":{"rendered":"<p style=\"text-align: justify;\">Consider an experiment whose sample space is S. For each event E of the sample space S, we assume that a number P(E) is defined and satisfies the following three axioms.<\/p>\n<p><strong>Axiom-1:<\/strong> 0 \u2264 P(E) \u2264 1<br \/>\n<strong>Axiom-2:<\/strong> P(S) = 1<br \/>\n<strong>Axiom-3:<\/strong> For any sequence of mutually exclusive events E1, E2, &#8230;(that is, events for which Ei \u2229 Ej = \u03c6 when i \u2260 j<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-6046 size-full\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2025\/08\/axioms-of-probability.jpg\" alt=\" Axioms of Probability\" width=\"479\" height=\"83\" srcset=\"https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/08\/axioms-of-probability.jpg 479w, https:\/\/www.madeeasy.in\/study\/wp-content\/uploads\/2025\/08\/axioms-of-probability-300x52.jpg 300w\" sizes=\"auto, (max-width: 479px) 100vw, 479px\" \/><\/p>\n<p><strong> Odds in Favour and Odds Against<\/strong><\/p>\n<p style=\"text-align: justify;\">In an event E, if the total number of possibilities of favorable cases is \u2018a\u2019 and the total number of unfavorable cases is\u00a0\u2018b\u2019.<\/p>\n<p>then, odds in favour = a\/b and odds against = b\/a<\/p>\n<p>If a + b is sample space, then<\/p>\n<p>P(E) = Odds in favor \/\u00a0Odds in favour + odds against<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Consider an experiment whose sample space is S. For each event E of the sample space S, we assume that<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1754,5],"tags":[1770,1769],"class_list":["post-6045","post","type-post","status-publish","format-standard","hentry","category-probability-and-statistics","category-ee","tag-odds-against","tag-odds-in-favour"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/6045","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=6045"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/6045\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=6045"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=6045"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=6045"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}