{"id":26761,"date":"2021-05-12T13:00:20","date_gmt":"2021-05-12T13:00:20","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=26761"},"modified":"2024-05-22T01:00:13","modified_gmt":"2024-05-22T01:00:13","slug":"%d0%b8%d1%81%d0%bf%d1%8b%d1%82%d0%b0%d0%bd%d0%b8%d0%b5-%d0%b1%d0%b5%d1%80%d0%bd%d1%83%d0%bb%d0%bb%d0%b8-%d0%b8-%d0%b1%d0%b8%d0%bd%d0%be%d0%bc%d0%b8%d0%b0%d0%bb%d1%8c%d0%bd%d0%be%d0%b5-%d1%80%d0%b0","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ru\/%d0%b8%d1%81%d0%bf%d1%8b%d1%82%d0%b0%d0%bd%d0%b8%d0%b5-%d0%b1%d0%b5%d1%80%d0%bd%d1%83%d0%bb%d0%bb%d0%b8-%d0%b8-%d0%b1%d0%b8%d0%bd%d0%be%d0%bc%d0%b8%d0%b0%d0%bb%d1%8c%d0%bd%d0%be%d0%b5-%d1%80%d0%b0\/","title":{"rendered":"\u0418\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0435 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 \u0438 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u0418\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0435 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 \u0438 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u0420\u0435\u0437\u044e\u043c\u0435<\/strong><br \/><em>\u0412 \u044d\u0442\u043e\u043c \u0443\u0440\u043e\u043a\u0435 \u043c\u044b \u0438\u0437\u0443\u0447\u0438\u043c \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u044e \u0438\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0439 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 \u0438 \u0438\u0445 \u0432\u043b\u0438\u044f\u043d\u0438\u0435 \u043d\u0430 \u0442\u0435\u043e\u0440\u0438\u044e \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439. \u041c\u044b \u043d\u0430\u0447\u043d\u0435\u043c \u0441 \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e\u0433\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0439 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438, \u0430 \u0437\u0430\u0442\u0435\u043c \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u044e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u0441\u043e\u0431\u044b\u0442\u0438\u0439. \u041f\u043e\u0441\u043b\u0435 \u0440\u0430\u0437\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u044f \u044d\u0442\u0438\u0445 \u0438\u0434\u0435\u0439 \u043c\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043c \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0442\u0435\u043e\u0440\u0435\u043c\u0443, \u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043d\u044f\u0442\u044c, \u043a\u0430\u043a \u043f\u043e\u0432\u0442\u043e\u0440\u0435\u043d\u0438\u0435 \u0438\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u044f \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 \u043f\u0440\u0438\u0432\u043e\u0434\u0438\u0442 \u043a \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0430\u043c \u0441 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u043c \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435\u043c. \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u0431\u0443\u0434\u0443\u0442 \u043f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u044b \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u0438 \u0443\u043a\u0440\u0435\u043f\u043b\u0435\u043d\u0438\u044f \u044d\u0442\u0438\u0445 \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u0439.<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>\u0426\u0415\u041b\u0418 \u041e\u0411\u0423\u0427\u0415\u041d\u0418\u042f:<\/strong><br \/>\n\u041f\u043e \u043e\u043a\u043e\u043d\u0447\u0430\u043d\u0438\u0438 \u044d\u0442\u043e\u0433\u043e \u0443\u0440\u043e\u043a\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442 \u0431\u0443\u0434\u0435\u0442 \u0441\u043f\u043e\u0441\u043e\u0431\u0435\u043d:\n<\/p>\n<ol>\n<li><strong>\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0442\u044c<\/strong> \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438 \u0438\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0439 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438, \u0432\u043a\u043b\u044e\u0447\u0430\u044f \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u043c\u0435\u0436\u0434\u0443 \u043f\u043e\u043f\u044b\u0442\u043a\u0430\u043c\u0438.<\/li>\n<li><strong>\u041f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c<\/strong> \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u0443\u044e \u043d\u043e\u0442\u0430\u0446\u0438\u044e \u0434\u043b\u044f \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u0441\u043e\u0431\u044b\u0442\u0438\u0439, \u0432\u043e\u0437\u043d\u0438\u043a\u0430\u044e\u0449\u0438\u0445 \u0438\u0437 \u0438\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0439 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438.<\/li>\n<li><strong>\u0420\u0430\u0437\u043b\u0438\u0447\u0430\u0442\u044c<\/strong> \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0435 \u0444\u043e\u0440\u043c\u044b \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 (2-\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c, 3-\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c, n-\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c) \u0438 \u043f\u043e\u043d\u0438\u043c\u0430\u0442\u044c \u0438\u0445 \u0441\u0432\u044f\u0437\u044c \u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u0432 \u0438\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u044f\u0445 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438.<\/li>\n<li><strong>\u041f\u043e\u043d\u0438\u043c\u0430\u0442\u044c<\/strong> \u0441\u0432\u044f\u0437\u044c \u043c\u0435\u0436\u0434\u0443 \u0438\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0435\u043c \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 \u0438 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u0435\u043e\u0440\u0435\u043c\u043e\u0439, \u0438 \u043a\u0430\u043a \u044d\u0442\u0430 \u0441\u0432\u044f\u0437\u044c \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0430 \u0434\u043b\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u0440\u044f\u0434\u0430 \u0443\u0441\u043f\u0435\u0445\u043e\u0432 \u0438 \u043d\u0435\u0443\u0434\u0430\u0447.<\/li>\n<li><strong>\u041f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c<\/strong> \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 (\u0438\u043b\u0438 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438) \u0434\u043b\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430 \u0443\u0441\u043f\u0435\u0445\u043e\u0432 \u0432 \u0441\u0435\u0440\u0438\u0438 \u043f\u043e\u043f\u044b\u0442\u043e\u043a.<\/li>\n<\/ol>\n<p><center><br \/>\n<strong><u>\u0421\u041e\u0414\u0415\u0420\u0416\u0410\u041d\u0418\u0415:<\/u><\/strong><br \/>\n<a href=\"#1\">\u0418\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0435 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438<\/a><br \/>\n<a href=\"#2\">\u0420\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0435 \u0444\u043e\u0440\u043c\u044b \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438<\/a><br \/>\n<a href=\"#3\">\u0418\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0435 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 \u0438 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0442\u0435\u043e\u0440\u0435\u043c\u0430<\/a><br \/>\n<a href=\"#4\">\u0411\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 (\u0438\u043b\u0438 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438) \u0438 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439<\/a><br \/>\n<a href=\"#5\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f:<\/a><br \/>\n<\/center><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/uyljDy0bcvU\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<p><a name=\"1\"><\/a><\/br><\/br><\/p>\n<h2>\u0418\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0435 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=uyljDy0bcvU&amp;t=103s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0418\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0435 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 &#8211; \u044d\u0442\u043e \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0439 \u044d\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442<\/span><\/strong><\/a> \u0434\u0438\u0445\u043e\u0442\u043e\u043c\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0441 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c\u044e \u0443\u0441\u043f\u0435\u0445\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p.<\/span><\/span> \u0415\u0441\u043b\u0438 \u0438\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0435 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 \u043f\u043e\u0432\u0442\u043e\u0440\u044f\u0435\u0442\u0441\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u0440\u0430\u0437 \u0438\u0434\u0435\u043d\u0442\u0438\u0447\u043d\u043e \u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e, \u0442\u043e\u0433\u0434\u0430 \u043f\u043e\u043b\u0443\u0447\u0430\u044e\u0442\u0441\u044f <strong>\u0441\u043e\u0431\u044b\u0442\u0438\u044f \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438:<\/strong> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/span> \u0443\u0441\u043f\u0435\u0445\u043e\u0432 \u0441\u0440\u0435\u0434\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u043f\u043e\u043f\u044b\u0442\u043e\u043a. \u042d\u0442\u0438 \u0441\u043e\u0431\u044b\u0442\u0438\u044f \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442\u0441\u044f <strong>\u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0441\u043e\u0431\u044b\u0442\u0438\u044f\u043c\u0438<\/strong> \u0438 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u044e\u0442\u0441\u044f \u043d\u043e\u0442\u0430\u0446\u0438\u0435\u0439<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Large \\displaystyle Bi(n;k;p)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0414\u0440\u0443\u0433\u043e\u0439 \u0432\u0430\u0436\u043d\u043e\u0439 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u043e\u0439 \u0438\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0439 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u043e, \u0447\u0442\u043e \u0432\u0441\u0435 \u043f\u043e\u043f\u044b\u0442\u043a\u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b \u0434\u0440\u0443\u0433 \u043e\u0442 \u0434\u0440\u0443\u0433\u0430.<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #000080;\">\u041f\u0420\u0418\u041c\u0415\u0420:<\/span> \u041c\u043d\u043e\u0433\u043e\u043a\u0440\u0430\u0442\u043d\u043e\u0435 \u0431\u0440\u043e\u0441\u0430\u043d\u0438\u0435 \u043a\u0443\u0431\u0438\u043a\u0430 \u0441 6 \u0433\u0440\u0430\u043d\u044f\u043c\u0438. \u041f\u0440\u0438\u043c\u0435\u0440\u044b \u0441\u043e\u0431\u044b\u0442\u0438\u0439 \u0442\u0438\u043f\u0430 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 \u0434\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u044d\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442\u0430:<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li><strong>\u0412\u044b\u043f\u0430\u0434\u0435\u043d\u0438\u0435 3 \u0442\u0443\u0437\u043e\u0432 \u0438\u0437 5 \u043f\u043e\u043f\u044b\u0442\u043e\u043a:<\/strong> \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442\u0441\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Bi(5;3;1\/6)<\/span><\/span><\/li>\n<li><strong>\u0412\u044b\u043f\u0430\u0434\u0435\u043d\u0438\u0435 7 \u0447\u0435\u0442\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b \u0438\u0437 12 \u043f\u043e\u043f\u044b\u0442\u043e\u043a:<\/strong> \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442\u0441\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Bi(12;7;1\/3)<\/span><\/span><\/li>\n<\/ul>\n<p><a name=\"2\"><\/a><\/br><\/br><\/p>\n<h3>\u0420\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0435 \u0444\u043e\u0440\u043c\u044b \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=uyljDy0bcvU&amp;t=283s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u041d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u043c\u0435\u0436\u0434\u0443 \u043f\u043e\u043f\u044b\u0442\u043a\u0430\u043c\u0438<\/span><\/strong><\/a> \u0432 \u0438\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0438 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 \u043d\u0435 \u0441\u043e\u0432\u0441\u0435\u043c \u0442\u0430 \u0436\u0435 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u044b \u0443\u0436\u0435 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u043b\u0438, \u044d\u0442\u043e \u0433\u043e\u0440\u0430\u0437\u0434\u043e \u0431\u043e\u043b\u0435\u0435 \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u043d\u0430\u044f \u0432\u0435\u0440\u0441\u0438\u044f. \u0427\u0442\u043e\u0431\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u0442\u044c \u044d\u0442\u043e \u0440\u0430\u0437\u043b\u0438\u0447\u0438\u0435, \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0442\u0438\u043f\u044b \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043c\u0435\u0436\u0434\u0443 \u0441\u043e\u0431\u044b\u0442\u0438\u044f\u043c\u0438<\/p>\n<h4>2-\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c<\/h4>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/toposuranos.com\/probabilidad-condicional-e-independencia-entre-eventos\/\" rel=\"noopener\" target=\"_blank\">\u041d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u044b \u0443\u0436\u0435 \u0437\u043d\u0430\u0435\u043c<\/a>, \u044d\u0442\u043e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u0441\u043e\u0431\u044b\u0442\u0438\u044f\u043c\u0438. \u041c\u044b \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c \u044d\u0442\u043e \u00ab2-\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c\u044e\u00bb. \u0412 \u044d\u0442\u0438\u0445 \u0442\u0435\u0440\u043c\u0438\u043d\u0430\u0445 \u043c\u044b \u0433\u043e\u0432\u043e\u0440\u0438\u043c, \u0447\u0442\u043e \u0441\u043e\u0431\u044b\u0442\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span> \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f 2-\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u043c\u0438, \u0435\u0441\u043b\u0438<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cap B) = P(A)P(B)<\/span><\/span><\/p>\n<h4>3-\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c<\/h4>\n<p style=\"text-align: justify; color: #000000;\">\u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e, 3-\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u0442\u0440\u0435\u0445 \u0441\u043e\u0431\u044b\u0442\u0438\u0439 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A,<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C<\/span><\/span> \u0447\u0435\u0440\u0435\u0437 \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cap B\\cap C) = P(A)P(B)P(C)<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0412\u0430\u0436\u043d\u043e \u043e\u0442\u043c\u0435\u0442\u0438\u0442\u044c, \u0447\u0442\u043e 2-\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u043c\u0435\u0436\u0434\u0443 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A,<\/span><\/span> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">B<\/span><\/span> \u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C<\/span><\/span> \u043d\u0435 \u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u043e\u0434\u0440\u0430\u0437\u0443\u043c\u0435\u0432\u0430\u0435\u0442 3-\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c, \u0445\u043e\u0442\u044f \u0432 \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u044d\u0442\u043e \u0432\u0435\u0440\u043d\u043e.<\/p>\n<h4>n-\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0432 \u0438\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u044f\u0445 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438<\/h4>\n<p style=\"text-align: justify; color: #000000;\">\u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0438\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f\u043c, n-\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u043d\u0430\u0431\u043e\u0440\u0430 \u0441\u043e\u0431\u044b\u0442\u0438\u0439 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">A_1, \\cdots, A_n<\/span><\/span> \u0447\u0435\u0440\u0435\u0437 \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Large \\displaystyle P\\left(\\bigcap_{i=1}^n A_i\\right) = \\prod_{i=1}^n P(A_i) <\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0418 \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e, \u0447\u0442\u043e:<\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(n-1)<\/span><\/span>-\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u043d\u0435 \u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u043e\u0434\u0440\u0430\u0437\u0443\u043c\u0435\u0432\u0430\u0435\u0442 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span>-\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span>-\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Longrightarrow<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">(n-1)<\/span><\/span>-\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u041f\u043e\u0432\u0442\u043e\u0440\u044b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span>, \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u043d\u044b\u0435 \u0432 \u0438\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0438 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438, \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span>-\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u043c\u0438.<\/p>\n<p><a name=\"3\"><\/a><\/br><\/br><\/p>\n<h2>\u0418\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0435 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 \u0438 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0442\u0435\u043e\u0440\u0435\u043c\u0430<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=uyljDy0bcvU&amp;t=478s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u044d\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442 \u0443\u0441\u043f\u0435\u0445\u0430 \u0438 \u043d\u0435\u0443\u0434\u0430\u0447\u0438<\/span><\/strong><\/a> \u0441 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c\u044e \u0443\u0441\u043f\u0435\u0445\u0430 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p<\/span><\/span>; \u0432 \u043a\u0430\u0436\u0434\u043e\u0439 \u043f\u043e\u043f\u044b\u0442\u043a\u0435, \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u0431\u0443\u0434\u0435\u0442 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1-p<\/span><\/span> \u043d\u0435\u0443\u0434\u0430\u0447\u0438. \u041e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u0447\u0442\u043e \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0443\u0441\u043f\u0435\u0445\u0430 \u0438\u043b\u0438 \u043d\u0435\u0443\u0434\u0430\u0447\u0438 \u0432 \u043a\u0430\u0436\u0434\u043e\u0439 \u043f\u043e\u043f\u044b\u0442\u043a\u0435 \u0440\u0430\u0432\u043d\u0430 1; \u0438 \u0442\u0430\u043a \u043a\u0430\u043a \u0432\u0441\u0435 \u043f\u043e\u043f\u044b\u0442\u043a\u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b, \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0443\u0441\u043f\u0435\u0445\u0430 \u0438\u043b\u0438 \u043d\u0435\u0443\u0434\u0430\u0447\u0438 \u0432 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u043f\u043e\u043f\u044b\u0442\u043a\u0430\u0445 \u0431\u0443\u0434\u0435\u0442 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1^n.<\/span><\/span> \u0418\u0437 \u044d\u0442\u043e\u0433\u043e \u0441\u043b\u0435\u0434\u0443\u0435\u0442:<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Large \\displaystyle 1 = 1^n = [p + (1-p)]^n = \\sum_{k=0}^n {{n}\\choose{k}} p^k(1-p)^{n-k} <\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0412 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u043c \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0430 <a href=\"https:\/\/toposuranos.com\/ejercicios-de-induccion-matematica-teorema-del-binomio-de-newton\/\" rel=\"noopener\" target=\"_blank\">\u0411\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430,<\/a> \u0438 \u0442\u0435\u0440\u043c\u0438\u043d\u044b \u0432\u043d\u0443\u0442\u0440\u0438 \u0441\u0443\u043c\u043c\u044b \u043c\u043e\u0436\u043d\u043e \u0438\u043d\u0442\u0435\u0440\u043f\u0440\u0435\u0442\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c:<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{k}}<\/span><\/span>: \u0447\u0438\u0441\u043b\u043e \u0441\u043f\u043e\u0441\u043e\u0431\u043e\u0432, \u043a\u043e\u0442\u043e\u0440\u044b\u043c\u0438 \u043c\u043e\u0433\u0443\u0442 \u043f\u0440\u043e\u0438\u0437\u043e\u0439\u0442\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/span> \u0443\u0441\u043f\u0435\u0445\u043e\u0432 \u043f\u0440\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u043f\u043e\u043f\u044b\u0442\u043a\u0430\u0445<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">p^k<\/span><\/span>: \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0433\u043e \u043d\u0430\u0441\u0442\u0443\u043f\u043b\u0435\u043d\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/span> \u0443\u0441\u043f\u0435\u0445\u043e\u0432<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(1-p)^{n-k}<\/span><\/span>: \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0433\u043e \u043d\u0430\u0441\u0442\u0443\u043f\u043b\u0435\u043d\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n-k<\/span><\/span> \u043d\u0435\u0443\u0434\u0430\u0447<\/li>\n<\/ul>\n<p style=\"text-align: justify; color: #000000;\">\u0421\u043e\u0431\u0440\u0430\u0432 \u044d\u0442\u0438 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u044b \u0432 \u0441\u0443\u043c\u043c\u0435, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c: \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0434\u043e\u0441\u0442\u0438\u0436\u0435\u043d\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k<\/span><\/span> \u0443\u0441\u043f\u0435\u0445\u043e\u0432 \u043f\u0440\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u043f\u043e\u043f\u044b\u0442\u043a\u0430\u0445; \u0438\u043b\u0438, \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e, \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0434\u043e\u0441\u0442\u0438\u0436\u0435\u043d\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n-k<\/span><\/span> \u043d\u0435\u0443\u0434\u0430\u0447 \u043f\u0440\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u043f\u043e\u043f\u044b\u0442\u043a\u0430\u0445.<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0420\u0430\u0437\u0434\u0435\u043b\u0438\u0432 \u043a\u0430\u0436\u0434\u044b\u0439 \u0442\u0435\u0440\u043c\u0438\u043d \u0441\u0443\u043c\u043c\u044b, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u0434\u043e\u0441\u0442\u0438\u0436\u0435\u043d\u0438\u044f:<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{0}} p^0(1-p)^{n-0} = (1-p)^n<\/span><\/span><\/td>\n<td>0 \u0443\u0441\u043f\u0435\u0445\u043e\u0432 \u043f\u0440\u0438 n \u043f\u043e\u043f\u044b\u0442\u043a\u0430\u0445<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{1}} p^1(1-\u043f)^{n-1} = n p(1-\u043f)^{n-1}<\/span><\/span><\/td>\n<td>1 \u0443\u0441\u043f\u0435\u0445 \u043f\u0440\u0438 n \u043f\u043e\u043f\u044b\u0442\u043a\u0430\u0445<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{2}} p^2(1-\u043f)^{n-2}<\/span><\/span><\/td>\n<td>2 \u0443\u0441\u043f\u0435\u0445\u0430 \u043f\u0440\u0438 n \u043f\u043e\u043f\u044b\u0442\u043a\u0430\u0445<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{k}} p^k(1-\u043f)^{n-k}<\/span><\/span><\/td>\n<td>k \u0443\u0441\u043f\u0435\u0445\u043e\u0432 \u043f\u0440\u0438 n \u043f\u043e\u043f\u044b\u0442\u043a\u0430\u0445<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vdots<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{n-1}} p^{n-1}(1-\u043f)^{n-(n-1)} = n p^{n-1}(1-\u043f)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n-1<\/span><\/span> \u0443\u0441\u043f\u0435\u0445\u043e\u0432 \u043f\u0440\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u043f\u043e\u043f\u044b\u0442\u043a\u0430\u0445<\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle {{n}\\choose{n}} p^{n}(1-\u043f)^{0} = p^{n}<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u0443\u0441\u043f\u0435\u0445\u043e\u0432 \u043f\u0440\u0438 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u043f\u043e\u043f\u044b\u0442\u043a\u0430\u0445<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u0418 \u0441\u0443\u043c\u043c\u0430 \u0432\u0441\u0435\u0445 \u044d\u0442\u0438\u0445 \u0442\u0435\u0440\u043c\u0438\u043d\u043e\u0432, \u043a\u0430\u043a \u043c\u044b \u0443\u0436\u0435 \u0432\u0438\u0434\u0435\u043b\u0438, \u0440\u0430\u0432\u043d\u0430 \u00ab1\u00bb. \u042d\u0442\u043e \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442, \u0447\u0442\u043e \u0432\u0441\u0435 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0435 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u044b \u0443\u0447\u0442\u0435\u043d\u044b.<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0418\u0437 \u044d\u0442\u043e\u0433\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f <strong>\u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0441\u043e\u0431\u044b\u0442\u0438\u044f \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438:<\/strong><\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\Large \\color{blue}{P(Bi(n;k;p)) = {{n}\\choose{k}}p^k(1-\u043f)^{n-k}}<\/span><\/span><\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0418\u043b\u0438 \u043c\u044b \u0442\u0430\u043a\u0436\u0435 \u0433\u043e\u0432\u043e\u0440\u0438\u043c, \u0447\u0442\u043e <strong>\u0447\u0438\u0441\u043b\u043e \u0443\u0441\u043f\u0435\u0445\u043e\u0432 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">X<\/span><\/span> \u0438\u043c\u0435\u0435\u0442 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435:<\/strong><\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\color{blue}{\\Large \\displaystyle X\\sim Bi(n;p) \\longmapsto P(X=x) = {{n}\\choose{x}}p^x(1-\u043f)^{n-x}}<\/span><\/span><\/p>\n<p><a name=\"4\"><\/a><\/br><\/br><\/p>\n<h3>\u0411\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 (\u0438\u043b\u0438 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438) \u0438 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439<\/h3>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=uyljDy0bcvU&amp;t=779s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0427\u0435\u0440\u0435\u0437 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435<\/span><\/strong><\/a> \u043c\u044b \u043d\u0430\u0447\u0438\u043d\u0430\u0435\u043c \u043f\u043e\u043d\u0438\u043c\u0430\u0442\u044c \u043f\u0435\u0440\u0432\u044b\u0435 \u043f\u043e\u043d\u044f\u0442\u0438\u044f \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0439 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439 \u0438 \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u0445 \u0432\u0435\u043b\u0438\u0447\u0438\u043d. \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u0430\u044f \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u0430\u044f \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430 \u0441\u0432\u044f\u0437\u0430\u043d\u0430 \u0441 \u0447\u0438\u0441\u043b\u043e\u043c \u0443\u0441\u043f\u0435\u0445\u043e\u0432, \u0438 \u0435\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u0435\u0440\u043c\u0438\u043d\u0430\u043c\u0438 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0442\u0435\u043e\u0440\u0435\u043c\u044b<\/p>\n<p style=\"text-align: center; color: #000000;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">{\\Large \\displaystyle P(X=x) = {{n}\\choose{x}}p^x(1-\u043f)^{n-x}}<\/span><\/span><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/36s4rcfQn7M\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<p><a name=\"5\"><\/a><\/br><\/br><\/p>\n<h2>\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f:<\/h2>\n<ol style=\"text-align: justify; color: #000000;\">\n<li>\u0411\u0440\u043e\u0441\u0430\u043d\u0438\u0435 \u043a\u0443\u0431\u0438\u043a\u0430 \u0441 6 \u0433\u0440\u0430\u043d\u044f\u043c\u0438 5 \u0440\u0430\u0437. \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0432\u044b\u043f\u0430\u0434\u0435\u043d\u0438\u044f 3 \u0447\u0435\u0442\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b.<\/li>\n<li>\u0411\u0440\u043e\u0441\u0430\u043d\u0438\u0435 \u043c\u043e\u043d\u0435\u0442\u044b 10 \u0440\u0430\u0437. \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0432\u044b\u043f\u0430\u0434\u0435\u043d\u0438\u044f \u043e\u0442 0 \u0434\u043e 10 \u043e\u0440\u043b\u043e\u0432 \u0438 \u043f\u043e\u0441\u0442\u0440\u043e\u0439\u0442\u0435 \u0433\u0440\u0430\u0444\u0438\u043a, \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u044e\u0449\u0438\u0439 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0430. \u041a\u0430\u043a \u0431\u0443\u0434\u0435\u0442 \u0432\u044b\u0433\u043b\u044f\u0434\u0435\u0442\u044c \u0433\u0440\u0430\u0444\u0438\u043a, \u0435\u0441\u043b\u0438 \u0443\u0432\u0435\u043b\u0438\u0447\u0438\u0442\u044c \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0431\u0440\u043e\u0441\u043a\u043e\u0432 \u0438 \u0438\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u044c \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0432\u044b\u043f\u0430\u0434\u0435\u043d\u0438\u044f \u0447\u0438\u0441\u043b\u0430 \u043e\u0440\u043b\u043e\u0432 \u043e\u0442 0 \u0434\u043e \u044d\u0442\u043e\u0433\u043e \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u0430 \u0431\u0440\u043e\u0441\u043a\u043e\u0432? \u0417\u0434\u0435\u0441\u044c \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043f\u043e\u043b\u0435\u0437\u0435\u043d Excel.<\/li>\n<li>\u0412 \u043b\u043e\u0442\u043e\u0442\u0440\u043e\u043d\u0435 \u0435\u0441\u0442\u044c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">s<\/span><\/span> \u0448\u0430\u0440\u0438\u043a\u043e\u0432, \u0438\u0437 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> \u0437\u043e\u043b\u043e\u0442\u044b\u0435, \u0430 \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0431\u0435\u043b\u044b\u0435. \u0412\u0441\u0435 \u0448\u0430\u0440\u0438\u043a\u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u0448\u0438\u0432\u0430\u044e\u0442\u0441\u044f, \u0438 \u043e\u0434\u0438\u043d \u0432\u044b\u0431\u0438\u0440\u0430\u0435\u0442\u0441\u044f \u0441\u043b\u0443\u0447\u0430\u0439\u043d\u044b\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0438 \u0432\u044b\u0438\u0433\u0440\u044b\u0448 \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442, \u043a\u043e\u0433\u0434\u0430 \u0432\u044b\u043f\u0430\u0434\u0430\u0435\u0442 \u0437\u043e\u043b\u043e\u0442\u043e\u0439 \u0448\u0430\u0440\u0438\u043a. \u0415\u0441\u043b\u0438 \u044d\u0442\u043e\u0442 \u044d\u043a\u0441\u043f\u0435\u0440\u0438\u043c\u0435\u043d\u0442 \u043f\u043e\u0432\u0442\u043e\u0440\u044f\u0435\u0442\u0441\u044f \u0438\u0434\u0435\u043d\u0442\u0438\u0447\u043d\u043e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">20<\/span><\/span> \u0440\u0430\u0437, \u043e\u0446\u0435\u043d\u0438\u0442\u0435 \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0435 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043f\u043e\u0431\u0435\u0434 \u0434\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\leq r\\leq s.<\/span><\/span> \u0417\u0434\u0435\u0441\u044c \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043f\u043e\u043b\u0435\u0437\u0435\u043d Excel.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u0418\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0435 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 \u0438 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0420\u0435\u0437\u044e\u043c\u0435\u0412 \u044d\u0442\u043e\u043c \u0443\u0440\u043e\u043a\u0435 \u043c\u044b \u0438\u0437\u0443\u0447\u0438\u043c \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u044e \u0438\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0439 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 \u0438 \u0438\u0445 \u0432\u043b\u0438\u044f\u043d\u0438\u0435 \u043d\u0430 \u0442\u0435\u043e\u0440\u0438\u044e \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439. \u041c\u044b \u043d\u0430\u0447\u043d\u0435\u043c \u0441 \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e\u0433\u043e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0438\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0439 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438, \u0430 \u0437\u0430\u0442\u0435\u043c \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u044e \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u0441\u043e\u0431\u044b\u0442\u0438\u0439. \u041f\u043e\u0441\u043b\u0435 \u0440\u0430\u0437\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u044f \u044d\u0442\u0438\u0445 \u0438\u0434\u0435\u0439 \u043c\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043c \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u0443\u044e \u0442\u0435\u043e\u0440\u0435\u043c\u0443, \u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043d\u044f\u0442\u044c, \u043a\u0430\u043a \u043f\u043e\u0432\u0442\u043e\u0440\u0435\u043d\u0438\u0435 \u0438\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u044f \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 \u043f\u0440\u0438\u0432\u043e\u0434\u0438\u0442 \u043a \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0430\u043c \u0441 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u043c \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435\u043c. \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u0431\u0443\u0434\u0443\u0442 \u043f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u044b [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":26419,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":5,"footnotes":""},"categories":[680,573],"tags":[],"class_list":["post-26761","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-680","category-573"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0418\u0441\u043f\u044b\u0442\u0430\u043d\u0438\u0435 \u0411\u0435\u0440\u043d\u0443\u043b\u043b\u0438 \u0438 \u0431\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u043e\u0435 \u0440\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 - toposuranos.com\/material<\/title>\n<meta name=\"description\" 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