{"id":993,"date":"2015-08-16T09:52:56","date_gmt":"2015-08-16T08:52:56","guid":{"rendered":"http:\/\/pcool.dyndns.org:8080\/statsbook\/?page_id=993"},"modified":"2025-06-27T08:17:07","modified_gmt":"2025-06-27T07:17:07","slug":"summary-probability","status":"publish","type":"page","link":"https:\/\/pcool.dyndns.org\/index.php\/summary-probability\/","title":{"rendered":"Probability"},"content":{"rendered":"\n<ul class=\"wp-block-list\">\n<li><strong>Probabilities that are dependent are multiplied<\/strong><\/li>\n\n\n\n<li><strong>Probabilities that are independent are added<\/strong><\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\(Probability(X) = \\frac{Number Of Combinations With X}{Total Number Of Combinations} \\)<script src=\"https:\/\/pcool.dyndns.org\/wp-includes\/js\/dist\/hooks.min.js?ver=dd5603f07f9220ed27f1\" id=\"wp-hooks-js\"><\/script>\n<script src=\"https:\/\/pcool.dyndns.org\/wp-includes\/js\/dist\/i18n.min.js?ver=c26c3dc7bed366793375\" id=\"wp-i18n-js\"><\/script>\n<script id=\"wp-i18n-js-after\">\nwp.i18n.setLocaleData( { 'text direction\\u0004ltr': [ 'ltr' ] } );\n\/\/# sourceURL=wp-i18n-js-after\n<\/script>\n<script  async src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjax\/2.7.7\/MathJax.js?config=TeX-MML-AM_CHTML\" id=\"mathjax-js\"><\/script>\n<\/div>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\(N = {t \\choose n} = \\frac{t!}{(t &#8211; n)! \\cdot n!} \\)\n<\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>t = total number of occurrences, n = number of occurrences<\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\(P = {t \\choose n} \\cdot c^n \\cdot (1-c)^{t &#8211; n} \\) (with putting back)<\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>t = total number of occurrences, n = number of occurrences, c = probability on single occurrence<\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-mathml-mathmlblock\">\\(P(X) = \\frac{{x \\choose a} \\cdot {y \\choose b} \\cdot {z \\choose c}} {t \\choose n} \\) (without putting back)<\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>t = total number of occurrences, n = number of occurrences, t = x + y + z, n = a = b + c<\/li>\n<\/ul>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-993","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages\/993","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/comments?post=993"}],"version-history":[{"count":2,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages\/993\/revisions"}],"predecessor-version":[{"id":4484,"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/pages\/993\/revisions\/4484"}],"wp:attachment":[{"href":"https:\/\/pcool.dyndns.org\/index.php\/wp-json\/wp\/v2\/media?parent=993"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}