{"id":26714,"date":"2021-04-19T13:00:16","date_gmt":"2021-04-19T13:00:16","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=26714"},"modified":"2024-05-21T21:07:16","modified_gmt":"2024-05-21T21:07:16","slug":"%d1%83%d1%81%d0%bb%d0%be%d0%b2%d0%bd%d0%b0%d1%8f-%d0%b2%d0%b5%d1%80%d0%be%d1%8f%d1%82%d0%bd%d0%be%d1%81%d1%82%d1%8c-%d0%b8-%d0%bd%d0%b5%d0%b7%d0%b0%d0%b2%d0%b8%d1%81%d0%b8%d0%bc%d0%be%d1%81%d1%82","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ru\/%d1%83%d1%81%d0%bb%d0%be%d0%b2%d0%bd%d0%b0%d1%8f-%d0%b2%d0%b5%d1%80%d0%be%d1%8f%d1%82%d0%bd%d0%be%d1%81%d1%82%d1%8c-%d0%b8-%d0%bd%d0%b5%d0%b7%d0%b0%d0%b2%d0%b8%d1%81%d0%b8%d0%bc%d0%be%d1%81%d1%82\/","title":{"rendered":"\u0423\u0441\u043b\u043e\u0432\u043d\u0430\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0441\u043e\u0431\u044b\u0442\u0438\u0439"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u0423\u0441\u043b\u043e\u0432\u043d\u0430\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0441\u043e\u0431\u044b\u0442\u0438\u0439<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u0420\u0435\u0437\u044e\u043c\u0435<\/strong><br \/><em>\u041d\u0430 \u044d\u0442\u043e\u043c \u0437\u0430\u043d\u044f\u0442\u0438\u0438 \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u044e \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0439 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u0438 \u0432\u0437\u0430\u0438\u043c\u043e\u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0441\u043e\u0431\u044b\u0442\u0438\u044f\u043c\u0438. \u041c\u044b \u043d\u0430\u0443\u0447\u0438\u043c\u0441\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c \u0443\u0441\u043b\u043e\u0432\u043d\u044b\u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0442\u044c \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0438\u043b\u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0441\u043e\u0431\u044b\u0442\u0438\u0439. \u041c\u044b \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043c \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u043d\u043e\u0441\u0442\u0438 \u043a\u0430\u0440\u0438\u0435\u0441\u0430 \u0443 \u043f\u043e\u0442\u0440\u0435\u0431\u0438\u0442\u0435\u043b\u0435\u0439 \u0441\u043b\u0430\u0434\u043e\u0441\u0442\u0435\u0439, \u0447\u0442\u043e\u0431\u044b \u043f\u0440\u043e\u0438\u043b\u043b\u044e\u0441\u0442\u0440\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u044d\u0442\u0438 \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u0438. \u0412 \u043a\u043e\u043d\u0446\u0435 \u0437\u0430\u043d\u044f\u0442\u0438\u044f \u0432\u044b \u0431\u0443\u0434\u0435\u0442\u0435 \u0447\u0435\u0442\u043a\u043e \u043f\u043e\u043d\u0438\u043c\u0430\u0442\u044c, \u043a\u0430\u043a \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c \u0443\u0441\u043b\u043e\u0432\u043d\u0443\u044e \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0438 \u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0435 \u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0435 \u0441\u043e\u0431\u044b\u0442\u0438\u044f.<\/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 \u0437\u0430\u043d\u044f\u0442\u0438\u044f \u0432\u044b \u0441\u043c\u043e\u0436\u0435\u0442\u0435:\n<\/p>\n<ol>\n<li><strong>\u041f\u043e\u043d\u044f\u0442\u044c<\/strong> \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0439 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u0438 \u0435\u0451 \u0441\u0432\u044f\u0437\u044c \u0441 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u0435\u043c \u0441\u043e\u0431\u044b\u0442\u0438\u0439 \u0438 \u0438\u043d\u0434\u0438\u0432\u0438\u0434\u0443\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044f\u043c\u0438.<\/li>\n<li><strong>\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c<\/strong> \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0438 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0430\u0441\u0441\u043e\u0446\u0438\u0430\u0446\u0438\u0438 \u043c\u0435\u0436\u0434\u0443 \u0441\u043e\u0431\u044b\u0442\u0438\u044f\u043c\u0438 \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0443\u0441\u043b\u043e\u0432\u043d\u044b\u0445 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439.<\/li>\n<li><strong>\u041f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c<\/strong> \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u0441\u043e\u0431\u044b\u0442\u0438\u0439.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>\u0421\u041e\u0414\u0415\u0420\u0416\u0410\u041d\u0418\u0415<\/u><\/strong><br \/>\n<a href=\"#1\">\u0423\u0421\u041b\u041e\u0412\u041d\u0410\u042f \u0412\u0415\u0420\u041e\u042f\u0422\u041d\u041e\u0421\u0422\u042c<\/a><br \/>\n<a href=\"#2\">\u0424\u041e\u0420\u041c\u0410\u041b\u042c\u041d\u041e\u0415 \u041e\u041f\u0420\u0415\u0414\u0415\u041b\u0415\u041d\u0418\u0415 \u0423\u0421\u041b\u041e\u0412\u041d\u041e\u0419 \u0412\u0415\u0420\u041e\u042f\u0422\u041d\u041e\u0421\u0422\u0418<\/a><br \/>\n<a href=\"#3\">\u0421\u0412\u042f\u0417\u042c \u041c\u0415\u0416\u0414\u0423 \u0421\u041e\u0411\u042b\u0422\u0418\u042f\u041c\u0418<\/a><br \/>\n<a href=\"#4\">\u041d\u0415\u0417\u0410\u0412\u0418\u0421\u0418\u041c\u041e\u0421\u0422\u042c \u0421\u041e\u0411\u042b\u0422\u0418\u0419 \u0418 \u0418\u0425 \u0414\u041e\u041f\u041e\u041b\u041d\u0415\u041d\u0418\u0419<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/rWzeKPNM-Ds\" 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 \/>\n<\/br><\/br><\/p>\n<h2>\u0423\u0441\u043b\u043e\u0432\u043d\u0430\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=rWzeKPNM-Ds&amp;t=132s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u041a\u0430\u043a\u043e\u0432\u0430 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u0441\u043e\u0431\u044b\u0442\u0438\u0435 A<\/span><\/strong><\/a> \u043f\u0440\u043e\u0438\u0437\u043e\u0439\u0434\u0435\u0442 \u043f\u0440\u0438 \u0443\u0441\u043b\u043e\u0432\u0438\u0438, \u0447\u0442\u043e \u0443\u0436\u0435 \u043f\u0440\u043e\u0438\u0437\u043e\u0448\u043b\u043e \u0441\u043e\u0431\u044b\u0442\u0438\u0435 B? \u0412\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u0442\u0430\u043a\u0438\u0445 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439 \u0438 \u0435\u0441\u0442\u044c \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u044f <strong>\u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0439 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438. <\/strong> \u0414\u0430\u043b\u0435\u0435 \u043c\u044b \u0438\u0437\u0443\u0447\u0438\u043c \u0443\u0441\u043b\u043e\u0432\u043d\u0443\u044e \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c, \u0435\u0451 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0438 \u043a\u0430\u043a \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u044d\u0442\u043e\u0433\u043e \u0432\u044b\u0432\u043e\u0434\u044f\u0442\u0441\u044f \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u043c\u0435\u0436\u0434\u0443 \u0441\u043e\u0431\u044b\u0442\u0438\u044f\u043c\u0438.<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u041f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u043c, \u0447\u0442\u043e \u043c\u044b \u0445\u043e\u0442\u0438\u043c \u0438\u0437\u043c\u0435\u0440\u0438\u0442\u044c \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u043d\u043e\u0441\u0442\u044c \u043a\u0430\u0440\u0438\u0435\u0441\u0430 \u0441\u0440\u0435\u0434\u0438 \u043e\u0431\u044b\u0447\u043d\u044b\u0445 \u043f\u043e\u0442\u0440\u0435\u0431\u0438\u0442\u0435\u043b\u0435\u0439 \u0441\u043b\u0430\u0434\u043e\u0441\u0442\u0435\u0439. \u0415\u0441\u043b\u0438 \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0432\u044b\u0431\u043e\u0440\u043a\u0443 \u0438\u0437 <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> \u0447\u0435\u043b\u043e\u0432\u0435\u043a <span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_N,<\/span> \u043c\u044b \u0443\u0432\u0438\u0434\u0438\u043c, \u0447\u0442\u043e \u0435\u0435 \u043c\u043e\u0436\u043d\u043e \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u0442\u044c \u043d\u0430 4 \u043f\u043e\u0434\u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0430:<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">A:=\\left\\{  {\u041b\u044e\u0434\u0438\\;\u0443\\;\u043a\u043e\u0442\u043e\u0440\u044b\u0445\\;\u0435\u0441\u0442\u044c\\;\u043a\u0430\u0440\u0438\u0435\u0441}\\right\\}<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">A^c:=\\left\\{{\u041b\u044e\u0434\u0438\\;\u0443\\;\u043a\u043e\u0442\u043e\u0440\u044b\u0445\\;\u041d\u0415\u0422\\;\u043a\u0430\u0440\u0438\u0435\u0441\u0430}\\right\\}<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">B:=\\left\\{  {\u041b\u044e\u0434\u0438\\;\u043a\u043e\u0442\u043e\u0440\u044b\u0435\\;\u0440\u0435\u0433\u0443\u043b\u044f\u0440\u043d\u043e\\;\u0435\u0434\u044f\u0442\\;\u0441\u043b\u0430\u0434\u043e\u0441\u0442\u0438}\\right\\}<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">B^c:=\\left\\{{\u041b\u044e\u0434\u0438\\;\u043a\u043e\u0442\u043e\u0440\u044b\u0435\\;\u041d\u0415\\;\u0435\u0434\u044f\u0442\\;\u0441\u043b\u0430\u0434\u043e\u0441\u0442\u0438\\;\u0440\u0435\u0433\u0443\u043b\u044f\u0440\u043d\u043e}\\right\\}<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify; color: #000000;\">\u0418\u0437 \u044d\u0442\u043e\u0433\u043e \u044f\u0441\u043d\u043e, \u0447\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">A\\cup A^c = \\Omega_N<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">B\\cup B^c = \\Omega_N,<\/span> \u043d\u043e <span class=\"katex-eq\" data-katex-display=\"false\">A\\cap B<\/span> \u043d\u0435 \u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u0443\u0441\u0442\u043e\u0435 \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e. \u041e\u0431\u0449\u0430\u044f \u0441\u0438\u0442\u0443\u0430\u0446\u0438\u044f \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0430 \u043d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c \u0440\u0438\u0441\u0443\u043d\u043a\u0435:<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-YZLH9zUJd2g\/YHzyLbaupDI\/AAAAAAAAE6c\/lpdThvvjvvsMYQqqIXelpU-Kcsd-uFWEwCLcBGAsYHQ\/s0\/probabilidad%2Bcondicional%2B1.PNG\" alt=\"\u0423\u0441\u043b\u043e\u0432\u043d\u0430\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c\" class=\" aligncenter lazyload\" width=\"339\" height=\"273\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-YZLH9zUJd2g\/YHzyLbaupDI\/AAAAAAAAE6c\/lpdThvvjvvsMYQqqIXelpU-Kcsd-uFWEwCLcBGAsYHQ\/s0\/probabilidad%2Bcondicional%2B1.PNG\" alt=\"\u0423\u0441\u043b\u043e\u0432\u043d\u0430\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c\" class=\" aligncenter lazyload\" width=\"339\" height=\"273\" \/><\/noscript><\/p>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=rWzeKPNM-Ds&amp;t=270s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0418\u0442\u0430\u043a, \u0435\u0441\u043b\u0438 \u043c\u044b \u0432\u0441\u043f\u043e\u043c\u043d\u0438\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438<\/span><\/strong><\/a> \u043a\u0430\u043a \u043f\u0440\u0435\u0434\u0435\u043b\u0430 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u0447\u0430\u0441\u0442\u043e\u0442, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0441\u043a\u0430\u0437\u0430\u0442\u044c, \u0447\u0442\u043e \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u0443 \u0447\u0435\u043b\u043e\u0432\u0435\u043a\u0430 \u0435\u0441\u0442\u044c \u043a\u0430\u0440\u0438\u0435\u0441 \u043f\u0440\u0438 \u0443\u0441\u043b\u043e\u0432\u0438\u0438, \u0447\u0442\u043e \u043f\u043e\u0434\u0442\u0432\u0435\u0440\u0436\u0434\u0435\u043d\u043e, \u0447\u0442\u043e \u043e\u043d \u043f\u043e\u0442\u0440\u0435\u0431\u043b\u044f\u0435\u0442 \u0441\u043b\u0430\u0434\u043e\u0441\u0442\u0438, <span class=\"katex-eq\" data-katex-display=\"false\">P(A|B)<\/span> \u0431\u0443\u0434\u0435\u0442:<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A|B) =\\displaystyle \\frac{\\#(A\\cap B)}{\\#B}<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c:<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cap B) = \\displaystyle \\frac{\\#(A\\cap B)}{\\#\\Omega_N}<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u21b3 <span class=\"katex-eq\" data-katex-display=\"false\">\\#(A\\cap B) = \\#\\Omega_N P(A\\cap B)<\/span>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(B) =\\displaystyle \\frac{\\#B}{\\#\\Omega_N} <\/span>\n<p style=\"text-align: justify; color: #000000;\">\u21b3 <span class=\"katex-eq\" data-katex-display=\"false\">\\#B = \\#\\Omega_N P(B)<\/span>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0435\u0441\u043b\u0438 \u043c\u044b \u0437\u0430\u043c\u0435\u043d\u0438\u043c \u044d\u0442\u0438 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0435 \u0434\u0432\u0430 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0432 <span class=\"katex-eq\" data-katex-display=\"false\">P(A|B)<\/span>, \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043c:<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A|B) = \\displaystyle \\frac{\\#\\Omega_N P(A\\cap B)}{\\#\\Omega_N P(B)} = \\frac{P(A\\cap B)}{P(B)} <\/span>\n<p style=\"text-align: justify; color: #000000;\">\u0421 \u044d\u0442\u0438\u043c \u043c\u044b \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #800000;\"><\/p>\n<p><a name=\"2\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u0424\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0439 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438<\/h2>\n<p><strong>\u041e\u041f\u0420\u0415\u0414\u0415\u041b\u0415\u041d\u0418\u0415:<\/strong><\/span> \u0412\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span>, \u043f\u0440\u0438 \u0443\u0441\u043b\u043e\u0432\u0438\u0438, \u0447\u0442\u043e \u043f\u0440\u043e\u0438\u0437\u043e\u0448\u043b\u043e <span class=\"katex-eq\" data-katex-display=\"false\">B,<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">P(A|B),<\/span> \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442\u0441\u044f \u0447\u0435\u0440\u0435\u0437 \u0441\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0435<\/p>\n<p style=\"text-align: center; color: #000000; background-color: #b0ffb0;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A|B) = \\displaystyle \\frac{P(A\\cap B)}{P(B)}<\/span>\u25a0<\/p>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=rWzeKPNM-Ds&amp;t=418s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0412 \u043f\u043e\u0432\u0441\u0435\u0434\u043d\u0435\u0432\u043d\u043e\u043c \u043c\u044b\u0448\u043b\u0435\u043d\u0438\u0438<\/span><\/strong><\/a> \u0447\u0430\u0441\u0442\u043e \u0432\u043e\u0437\u043d\u0438\u043a\u0430\u0435\u0442 \u043f\u0443\u0442\u0430\u043d\u0438\u0446\u0430 \u043c\u0435\u0436\u0434\u0443 <span class=\"katex-eq\" data-katex-display=\"false\">P(A|B)<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">P(B|A).<\/span> \u0427\u0442\u043e\u0431\u044b \u043f\u0440\u043e\u044f\u0441\u043d\u0438\u0442\u044c \u044d\u0442\u0443 \u0440\u0430\u0437\u043d\u0438\u0446\u0443, \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440 \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u043a\u0440\u0430\u0439\u043d\u0435\u0433\u043e \u0441\u043b\u0443\u0447\u0430\u044f: \u0417\u0430\u043c\u0435\u0442\u0438\u043c, \u0447\u0442\u043e \u0432 \u0442\u043e \u0432\u0440\u0435\u043c\u044f \u043a\u0430\u043a \u0443 \u0432\u0441\u0435\u0445 \u0444\u0443\u0442\u0431\u043e\u043b\u0438\u0441\u0442\u043e\u0432 \u0435\u0441\u0442\u044c \u0434\u0432\u0435 \u043d\u043e\u0433\u0438, \u0442\u043e\u043b\u044c\u043a\u043e \u043d\u0435\u0437\u043d\u0430\u0447\u0438\u0442\u0435\u043b\u044c\u043d\u0430\u044f \u0447\u0430\u0441\u0442\u044c \u043b\u044e\u0434\u0435\u0439 \u0441 \u0434\u0432\u0443\u043c\u044f \u043d\u043e\u0433\u0430\u043c\u0438 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0444\u0443\u0442\u0431\u043e\u043b\u0438\u0441\u0442\u0430\u043c\u0438.<\/p>\n<p><a name=\"3\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u0421\u0432\u044f\u0437\u044c \u043c\u0435\u0436\u0434\u0443 \u0441\u043e\u0431\u044b\u0442\u0438\u044f\u043c\u0438<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=rWzeKPNM-Ds&amp;t=534s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u041f\u0440\u043e\u0434\u043e\u043b\u0436\u0430\u044f \u043f\u0440\u0438\u043c\u0435\u0440 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u043d\u043e\u0441\u0442\u0438<\/span><\/strong><\/a> \u043a\u0430\u0440\u0438\u0435\u0441\u0430 \u0441\u0440\u0435\u0434\u0438 \u043b\u044e\u0434\u0435\u0439, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0440\u0435\u0433\u0443\u043b\u044f\u0440\u043d\u043e \u043f\u043e\u0442\u0440\u0435\u0431\u043b\u044f\u044e\u0442 \u0441\u043b\u0430\u0434\u043e\u0441\u0442\u0438. \u0415\u0441\u043b\u0438 \u043f\u043e\u0442\u0440\u0435\u0431\u043b\u0435\u043d\u0438\u0435 \u0441\u043b\u0430\u0434\u043e\u0441\u0442\u0435\u0439 \u0434\u0435\u043b\u0430\u0435\u0442 \u043b\u044e\u0434\u0435\u0439 \u0431\u043e\u043b\u0435\u0435 \u0441\u043a\u043b\u043e\u043d\u043d\u044b\u043c\u0438 \u043a \u043a\u0430\u0440\u0438\u0435\u0441\u0443, \u0442\u043e \u0434\u043e\u043b\u0436\u043d\u043e \u0431\u044b\u0442\u044c:<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A|B) \\gt P(A).<\/span>\u0417\u0434\u0435\u0441\u044c \u043c\u044b \u0432\u0438\u0434\u0438\u043c, \u0447\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u0443\u0441\u0438\u043b\u0438\u0432\u0430\u0435\u0442 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span>, \u0438 \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0433\u043e\u0432\u043e\u0440\u0438\u043c, \u0447\u0442\u043e \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 <strong>\u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0441\u043e\u0446\u0438\u0430\u0446\u0438\u044f<\/strong> \u043c\u0435\u0436\u0434\u0443 \u0441\u043e\u0431\u044b\u0442\u0438\u044f\u043c\u0438.<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0415\u0441\u043b\u0438, \u043d\u0430\u043e\u0431\u043e\u0440\u043e\u0442, \u043f\u043e\u0442\u0440\u0435\u0431\u043b\u0435\u043d\u0438\u0435 \u0441\u043b\u0430\u0434\u043e\u0441\u0442\u0435\u0439 \u043f\u0440\u0435\u0434\u043e\u0442\u0432\u0440\u0430\u0449\u0430\u0435\u0442 \u043a\u0430\u0440\u0438\u0435\u0441, \u0442\u043e \u0434\u043e\u043b\u0436\u043d\u043e \u0431\u044b\u0442\u044c:<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A|B) \\lt P(A).<\/span>\u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u043f\u043e\u0434\u0430\u0432\u043b\u044f\u0435\u0442 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span>, \u0438 \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0433\u043e\u0432\u043e\u0440\u0438\u043c, \u0447\u0442\u043e \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 <strong>\u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u0430\u044f \u0430\u0441\u0441\u043e\u0446\u0438\u0430\u0446\u0438\u044f<\/strong> \u043c\u0435\u0436\u0434\u0443 \u0441\u043e\u0431\u044b\u0442\u0438\u044f\u043c\u0438.<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0418 \u0435\u0441\u043b\u0438 \u043c\u0435\u0436\u0434\u0443 \u044d\u0442\u0438\u043c\u0438 \u0434\u0432\u0443\u043c\u044f \u0441\u043e\u0431\u044b\u0442\u0438\u044f\u043c\u0438 \u043d\u0435\u0442 \u043d\u0438\u043a\u0430\u043a\u043e\u0439 \u0441\u0432\u044f\u0437\u0438, \u043d\u0438 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0439, \u043d\u0438 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439, \u0442\u043e \u0434\u043e\u043b\u0436\u043d\u043e \u0431\u044b\u0442\u044c:<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A|B) = P(A).<\/span>\u041e\u0442\u0441\u044e\u0434\u0430 \u0441\u043b\u0435\u0434\u0443\u0435\u0442, \u0447\u0442\u043e \u0432\u043e \u043c\u043d\u043e\u0433\u0438\u0445 \u0443\u0447\u0435\u0431\u043d\u0438\u043a\u0430\u0445 \u043f\u043e \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u044d\u0442\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043a\u0430\u043a \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435:<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(A|B) = P(A)<\/span><\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\equiv<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{P(A\\cap B)}{P(B)} = P(A)<\/span><\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\equiv<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">P(A\\cap B)= P(A) P(B)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u042d\u0442\u043e\u0442 \u0432\u044b\u0432\u043e\u0434 \u043f\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u0441\u0432\u044f\u0437\u044c \u043c\u0435\u0436\u0434\u0443 \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0439 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c\u044e \u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c\u044e \u0441\u043e\u0431\u044b\u0442\u0438\u0439.<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #800000;\"><strong>\u041e\u041f\u0420\u0415\u0414\u0415\u041b\u0415\u041d\u0418\u0415:<\/strong><\/span> \u0414\u0432\u0430 \u0441\u043e\u0431\u044b\u0442\u0438\u044f <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442\u0441\u044f <strong>\u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u043c\u0438<\/strong>, \u0435\u0441\u043b\u0438 \u043e\u043d\u0438 \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u044e\u0442 \u0441\u043e\u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044e<\/p>\n<p style=\"text-align: center; color: #000000; background-color: #b0ffb0;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\color{black}{P(A\\cap B)= P(A) P(B)}<\/span>\u25a0<\/p>\n<p><a name=\"4\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u041d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0441\u043e\u0431\u044b\u0442\u0438\u0439 \u0438 \u0438\u0445 \u0434\u043e\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u0439<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=rWzeKPNM-Ds&amp;t=662s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u041d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0434\u0432\u0443\u0445 \u0441\u043e\u0431\u044b\u0442\u0438\u0439<\/span><\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u0430 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">B^c,<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">A^c<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">B,<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">A^c<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">B^c.<\/span>\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #000080;\"><strong>\u0414\u041e\u041a\u0410\u0417\u0410\u0422\u0415\u041b\u042c\u0421\u0422\u0412\u041e<\/strong><\/span><\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(1)<\/span> <\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{P(A\\cap B) = P(A)P(B)\\}\\vdash P(A\\cap B) = P(A)P(B)<\/span><\/td>\n<td>; \u041f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u0435<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(2)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{P(A\\cap B) = P(A)P(B)\\}\\vdash P(A\\cap B^c) = P(A\\setminus B)<\/span><\/td>\n<td>; \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\"> A\\cap B^c := A\\setminus B <\/span><\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(3)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> \\{P(A\\cap B) = P(A)P(B)\\}\\vdash P(A\\setminus B)= P(A) - P(A\\cap B)<\/span><\/td>\n<td>; <a href=\"https:\/\/toposuranos.com\/probabilidades-y-estadistica-ejercicios-de-teoria\/\" rel=\"noopener\" target=\"_blank\">\u0421\u043c. \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f 2<\/a><\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(4)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{P(A\\cap B) = P(A)P(B)\\}\\vdash P(A\\cap B^c)= P(A) - P(A\\cap B)<\/span><\/td>\n<td>; \u0418\u0437 (2) \u0438 (3)<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(5)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{P(A\\cap B) = P(A)P(B)\\}\\vdash P(A\\cap B^c)= P(A) - P(A)P(B)<\/span><\/td>\n<td>; \u0418\u0437 (1) \u0438 (4)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{P(A\\cap B) = P(A)P(B)\\}\\vdash P(A\\cap B^c)= P(A)(1 -P(B))<\/span><\/td>\n<td>; \u0424\u0430\u043a\u0442\u043e\u0440\u0438\u0437\u0430\u0446\u0438\u044f \u043f\u043e <span class=\"katex-eq\" data-katex-display=\"false\">P(A)<\/span><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\color{red}{\\{P(A\\cap B) = P(A)P(B)\\}\\vdash P(A\\cap B^c)= P(A)P(B^c)}<\/span><\/td>\n<td>; <a href=\"https:\/\/toposuranos.com\/probabilidades-y-estadistica-ejercicios-de-teoria\/\" rel=\"noopener\" target=\"_blank\">\u0421\u043c. \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f 1<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u042d\u0442\u043e \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0447\u0438\u0442\u0430\u0435\u0442\u0441\u044f \u0442\u0430\u043a: \u00ab\u0418\u0437 \u0442\u043e\u0433\u043e, \u0447\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b, \u0441\u043b\u0435\u0434\u0443\u0435\u0442, \u0447\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">B^c<\/span> \u0442\u0430\u043a\u0436\u0435 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b.<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u0414\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u0441\u0442\u0432\u043e \u0432 \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u043c \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438 \u0434\u0435\u043b\u0430\u0435\u0442\u0441\u044f \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e.<\/p>\n<table style=\"text-align: justify; color: #000000;\">\n<tbody>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(1)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{P(A\\cap B^c) = P(A)P(B^c)\\}\\vdash P(A\\cap B^c) = P(A)P(B^c)<\/span><\/td>\n<td>; \u041f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u0435<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{P(A\\cap B^c) = P(A)P(B^c)\\}\\vdash P(A\\cap B^c) = P(A)(1 - P(B))<\/span><\/td>\n<td>; <a href=\"https:\/\/toposuranos.com\/probabilidades-y-estadistica-ejercicios-de-teoria\/\" rel=\"noopener\" target=\"_blank\">\u0421\u043c. \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f 1<\/a><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{P(A\\cap B^c) = P(A)P(B^c)\\}\\vdash P(A\\cap B^c) = P(A) - P(A)P(B)<\/span><\/td>\n<td>; \u0412\u044b\u043f\u043e\u043b\u043d\u044f\u044f \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u0432 \u043f\u0440\u0430\u0432\u043e\u0439 \u0447\u0430\u0441\u0442\u0438.<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(2)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{P(A\\cap B^c) = P(A)P(B^c)\\}\\vdash P(A\\cap B^c) = P(A\\setminus B)<\/span><\/td>\n<td>; \u041f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">A\\setminus B := A\\cap B^c<\/span>.<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(3)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{P(A\\cap B^c) = P(A)P(B^c)\\}\\vdash P(A\\setminus B) = P(A) - P(A\\cap B) <\/span><\/td>\n<td>; <a href=\"https:\/\/toposuranos.com\/probabilidades-y-estadistica-ejercicios-de-teoria\/\" rel=\"noopener\" target=\"_blank\">\u0421\u043c. \u0440\u0430\u0437\u0432\u0438\u0442\u0438\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f 2<\/a><\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(4)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\{P(A\\cap B^c) = P(A)P(B^c)\\}\\vdash P(A) - P(A)P(B) = P(A) - P(A\\cap B) <\/span><\/td>\n<td>; \u0418\u0437 (1), (2) \u0438 (3)<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\color{red}{\\{P(A\\cap B^c) = P(A)P(B^c)\\}\\vdash P(A)P(B) = P(A\\cap B)} <\/span><\/td>\n<td>; \u0423\u0441\u0442\u0440\u0430\u043d\u044f\u044f \u043f\u043e\u0434\u043e\u0431\u043d\u044b\u0435 \u0442\u0435\u0440\u043c\u0438\u043d\u044b<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u0418 \u044d\u0442\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0447\u0438\u0442\u0430\u0435\u0442\u0441\u044f \u0442\u0430\u043a: \u00ab\u0418\u0437 \u0442\u043e\u0433\u043e, \u0447\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">B^c<\/span> \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b, \u0441\u043b\u0435\u0434\u0443\u0435\u0442, \u0447\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u0442\u0430\u043a\u0436\u0435 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b.<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u0438\u0437 \u044d\u0442\u0438\u0445 \u0434\u0432\u0443\u0445 \u0440\u0430\u0441\u0441\u0443\u0436\u0434\u0435\u043d\u0438\u0439 \u0441\u043b\u0435\u0434\u0443\u0435\u0442 \u0434\u043e\u043a\u0430\u0437\u0430\u043d\u043d\u0430\u044f \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u043e\u0441\u0442\u044c \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0441 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u0441 <span class=\"katex-eq\" data-katex-display=\"false\">B^c.<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u041e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0434\u043e\u043a\u0430\u0437\u0430\u043d\u043d\u044b\u0435 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u043e\u0441\u0442\u0438 \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u044b\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c. \u041e\u043d\u0438 \u043e\u0441\u0442\u0430\u043d\u0443\u0442\u0441\u044f \u0432 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u0432\u044b\u0437\u043e\u0432\u0430 \u0434\u043b\u044f \u0447\u0438\u0442\u0430\u0442\u0435\u043b\u044f &gt;:D<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0423\u0441\u043b\u043e\u0432\u043d\u0430\u044f \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c \u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0441\u043e\u0431\u044b\u0442\u0438\u0439 \u0420\u0435\u0437\u044e\u043c\u0435\u041d\u0430 \u044d\u0442\u043e\u043c \u0437\u0430\u043d\u044f\u0442\u0438\u0438 \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u044e \u0443\u0441\u043b\u043e\u0432\u043d\u043e\u0439 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u0438 \u0432\u0437\u0430\u0438\u043c\u043e\u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0441\u043e\u0431\u044b\u0442\u0438\u044f\u043c\u0438. \u041c\u044b \u043d\u0430\u0443\u0447\u0438\u043c\u0441\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c \u0443\u0441\u043b\u043e\u0432\u043d\u044b\u0435 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0438 \u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0442\u044c \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0438\u043b\u0438 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u044c \u0441\u043e\u0431\u044b\u0442\u0438\u0439. \u041c\u044b \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043c \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b, \u0442\u0430\u043a\u0438\u0435 \u043a\u0430\u043a \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u0435 \u0440\u0430\u0441\u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0435\u043d\u043d\u043e\u0441\u0442\u0438 \u043a\u0430\u0440\u0438\u0435\u0441\u0430 \u0443 \u043f\u043e\u0442\u0440\u0435\u0431\u0438\u0442\u0435\u043b\u0435\u0439 \u0441\u043b\u0430\u0434\u043e\u0441\u0442\u0435\u0439, \u0447\u0442\u043e\u0431\u044b \u043f\u0440\u043e\u0438\u043b\u043b\u044e\u0441\u0442\u0440\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u044d\u0442\u0438 \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u0438. \u0412 \u043a\u043e\u043d\u0446\u0435 \u0437\u0430\u043d\u044f\u0442\u0438\u044f \u0432\u044b \u0431\u0443\u0434\u0435\u0442\u0435 \u0447\u0435\u0442\u043a\u043e \u043f\u043e\u043d\u0438\u043c\u0430\u0442\u044c, \u043a\u0430\u043a \u043f\u0440\u0438\u043c\u0435\u043d\u044f\u0442\u044c \u0443\u0441\u043b\u043e\u0432\u043d\u0443\u044e \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u044c 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