{"id":26699,"date":"2021-04-19T13:00:02","date_gmt":"2021-04-19T13:00:02","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=26699"},"modified":"2024-05-21T12:26:42","modified_gmt":"2024-05-21T12:26:42","slug":"%e6%9d%a1%e4%bb%b6%e6%a6%82%e7%8e%87%e4%b8%8e%e4%ba%8b%e4%bb%b6%e7%8b%ac%e7%ab%8b%e6%80%a7","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e6%9d%a1%e4%bb%b6%e6%a6%82%e7%8e%87%e4%b8%8e%e4%ba%8b%e4%bb%b6%e7%8b%ac%e7%ab%8b%e6%80%a7\/","title":{"rendered":"\u6761\u4ef6\u6982\u7387\u4e0e\u4e8b\u4ef6\u72ec\u7acb\u6027"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u6761\u4ef6\u6982\u7387\u4e0e\u4e8b\u4ef6\u72ec\u7acb\u6027<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u6458\u8981<\/strong><br \/><em>\u5728\u672c\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u63a2\u8ba8\u6761\u4ef6\u6982\u7387\u7684\u6982\u5ff5\u4ee5\u53ca\u4e8b\u4ef6\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u3002\u6211\u4eec\u5c06\u5b66\u4e60\u5982\u4f55\u8ba1\u7b97\u6761\u4ef6\u6982\u7387\u5e76\u786e\u5b9a\u4e8b\u4ef6\u4e4b\u95f4\u7684\u4f9d\u8d56\u6027\u6216\u72ec\u7acb\u6027\u3002\u6211\u4eec\u5c06\u901a\u8fc7\u5b9e\u9645\u4f8b\u5b50\uff0c\u5982\u7814\u7a76\u7cd6\u679c\u6d88\u8d39\u8005\u4e2d\u9f8b\u9f7f\u7684\u60a3\u75c5\u7387\uff0c\u6765\u8bf4\u660e\u8fd9\u4e9b\u6982\u5ff5\u3002\u6700\u540e\uff0c\u4f60\u5c06\u6e05\u695a\u5730\u7406\u89e3\u5982\u4f55\u5e94\u7528\u6761\u4ef6\u6982\u7387\u5e76\u5206\u6790\u4f9d\u8d56\u548c\u72ec\u7acb\u4e8b\u4ef6\u3002<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u4e60\u76ee\u6807\uff1a<\/strong><br \/>\n\u5728\u672c\u8282\u8bfe\u7ed3\u675f\u65f6\uff0c\u4f60\u5c06\u80fd\u591f\uff1a\n<\/p>\n<ol>\n<li><strong>\u7406\u89e3<\/strong>\u6761\u4ef6\u6982\u7387\u7684\u5b9a\u4e49\u53ca\u5176\u4e0e\u4e8b\u4ef6\u4ea4\u96c6\u548c\u4e2a\u4f53\u6982\u7387\u7684\u5173\u7cfb\u3002<\/li>\n<li><strong>\u8bc6\u522b<\/strong>\u901a\u8fc7\u6bd4\u8f83\u6761\u4ef6\u6982\u7387\u786e\u5b9a\u4e8b\u4ef6\u4e4b\u95f4\u7684\u6b63\u8d1f\u5173\u8054\u3002<\/li>\n<li><strong>\u68c0\u9a8c<\/strong>\u4e0d\u540c\u4e8b\u4ef6\u4e4b\u95f4\u7684\u72ec\u7acb\u6027\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>\u5185\u5bb9\u7d22\u5f15<\/u><\/strong><br \/>\n<a href=\"#1\">\u6761\u4ef6\u6982\u7387<\/a><br \/>\n<a href=\"#2\">\u6761\u4ef6\u6982\u7387\u7684\u6b63\u5f0f\u5b9a\u4e49<\/a><br \/>\n<a href=\"#3\">\u4e8b\u4ef6\u4e4b\u95f4\u7684\u5173\u7cfb<\/a><br \/>\n<a href=\"#4\">\u4e8b\u4ef6\u72ec\u7acb\u6027\u4e0e\u4e8b\u4ef6\u8865\u96c6\u7684\u72ec\u7acb\u6027<\/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>\u6761\u4ef6\u6982\u7387<\/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;\">\u4e8b\u4ef6A<\/span><\/strong><\/a>\u5728\u4e8b\u4ef6B\u5df2\u7ecf\u53d1\u751f\u7684\u60c5\u51b5\u4e0b\u53d1\u751f\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f\u8fd9\u79cd\u6982\u7387\u7684\u8ba1\u7b97\u6d89\u53ca<strong>\u6761\u4ef6\u6982\u7387<\/strong>\u7684\u6982\u5ff5\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u5c06\u7814\u7a76\u6761\u4ef6\u6982\u7387\u3001\u5176\u5b9a\u4e49\u4ee5\u53ca\u5982\u4f55\u4ece\u4e2d\u63a8\u65ad\u4e8b\u4ef6\u4e4b\u95f4\u7684\u4f9d\u8d56\u6027\u548c\u72ec\u7acb\u6027\u5173\u7cfb\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5047\u8bbe\u6211\u4eec\u60f3\u8981\u6d4b\u91cf\u5e38\u89c4\u7cd6\u679c\u6d88\u8d39\u8005\u4e2d\u9f8b\u9f7f\u7684\u60a3\u75c5\u7387\u3002\u5982\u679c\u6211\u4eec\u68c0\u67e5\u4e00\u4e2a\u7531<span class=\"katex-eq\" data-katex-display=\"false\">N<\/span>\u4e2a\u4eba\u7ec4\u6210\u7684\u6837\u672c\u7a7a\u95f4<span class=\"katex-eq\" data-katex-display=\"false\">\\Omega_N,<\/span>\u6211\u4eec\u4f1a\u770b\u5230\u5b83\u53ef\u4ee5\u5206\u62104\u4e2a\u5b50\u96c6\uff1a<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li><span class=\"katex-eq\" data-katex-display=\"false\">A:=\\left\\{  {\u6709\u9f8b\u9f7f\u7684\u4eba}\\right\\}<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">A^c:=\\left\\{{\u6ca1\u6709\u9f8b\u9f7f\u7684\u4eba}\\right\\}<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">B:=\\left\\{  {\u7ecf\u5e38\u5403\u7cd6\u679c\u7684\u4eba}\\right\\}<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">B^c:=\\left\\{{\u4e0d\u7ecf\u5e38\u5403\u7cd6\u679c\u7684\u4eba}\\right\\}<\/span><\/li>\n<\/ul>\n<p style=\"text-align: justify; color: #000000;\">\u7531\u6b64\u53ef\u77e5\uff0c<span class=\"katex-eq\" data-katex-display=\"false\">A\\cup A^c = \\Omega_N<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">B\\cup B^c = \\Omega_N,<\/span> \u4f46 <span class=\"katex-eq\" data-katex-display=\"false\">A\\cap B<\/span> \u4e0d\u4e00\u5b9a\u4e3a\u7a7a\u3002\u4e00\u822c\u60c5\u51b5\u4e0b\u5982\u56fe\u6240\u793a\uff1a<\/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=\"\u6761\u4ef6\u6982\u7387\" 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=\"\u6761\u4ef6\u6982\u7387\" 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;\">\u90a3\u4e48\uff0c\u5982\u679c\u6211\u4eec\u8bb0\u4f4f\u6982\u7387\u7684\u5b9a\u4e49<\/span><\/strong><\/a>\u4e3a\u76f8\u5bf9\u9891\u7387\u7684\u6781\u9650\uff0c\u6211\u4eec\u53ef\u4ee5\u8bf4\u4e00\u4e2a\u4eba\u5728\u5df2\u7ecf\u786e\u8ba4\u5176\u5403\u7cd6\u679c\u7684\u60c5\u51b5\u4e0b\u6709\u9f8b\u9f7f\u7684\u6982\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">P(A|B)<\/span> \u5c06\u662f\uff1a<\/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;\">\u53e6\u4e00\u65b9\u9762\uff0c\u6709\uff1a<\/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;\">\u56e0\u6b64\uff0c\u5982\u679c\u5c06\u8fd9\u4e24\u4e2a\u8868\u8fbe\u5f0f\u4ee3\u5165 <span class=\"katex-eq\" data-katex-display=\"false\">P(A|B)<\/span>\uff0c\u6211\u4eec\u5c06\u5f97\u5230\uff1a<\/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;\">\u7531\u6b64\u5f97\u51fa\u4ee5\u4e0b\u5b9a\u4e49\uff1a<\/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>\u6761\u4ef6\u6982\u7387\u7684\u6b63\u5f0f\u5b9a\u4e49<\/h2>\n<p><strong>\u5b9a\u4e49\uff1a<\/strong><\/span> \u5728\u4e8b\u4ef6 <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u5df2\u7ecf\u53d1\u751f\u7684\u60c5\u51b5\u4e0b\uff0c\u4e8b\u4ef6 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u7684\u6982\u7387 <span class=\"katex-eq\" data-katex-display=\"false\">P(A|B),<\/span> \u5b9a\u4e49\u4e3a\uff1a<\/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;\">\u5728\u65e5\u5e38\u601d\u7ef4\u4e2d\uff0c\u5f80\u5f80<\/span><\/strong><\/a>\u4f1a\u5c06 <span class=\"katex-eq\" data-katex-display=\"false\">P(A|B)<\/span> \u4e0e <span class=\"katex-eq\" data-katex-display=\"false\">P(B|A)<\/span> \u6df7\u6dc6\u3002\u4e3a\u4e86\u6f84\u6e05\u8fd9\u4e00\u533a\u522b\uff0c\u6211\u4eec\u6765\u770b\u4e00\u4e2a\u6781\u7aef\u60c5\u51b5\u4e0b\u7684\u4f8b\u5b50\uff1a\u6ce8\u610f\uff0c\u867d\u7136\u6240\u6709\u7684\u8db3\u7403\u8fd0\u52a8\u5458\u90fd\u6709\u4e24\u6761\u817f\uff0c\u4f46\u53ea\u6709\u6781\u5c11\u6570\u6709\u4e24\u6761\u817f\u7684\u4eba\u662f\u8db3\u7403\u8fd0\u52a8\u5458\u3002<\/p>\n<p><a name=\"3\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u4e8b\u4ef6\u4e4b\u95f4\u7684\u5173\u7cfb<\/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;\">\u7ee7\u7eed\u4ee5\u5e38\u89c4\u7cd6\u679c\u6d88\u8d39\u8005\u4e2d\u9f8b\u9f7f\u60a3\u75c5\u7387\u7684\u4f8b\u5b50<\/span><\/strong><\/a>\u3002\u5982\u679c\u5403\u7cd6\u679c\u4f1a\u8ba9\u4eba\u66f4\u5bb9\u6613\u5f97\u9f8b\u9f7f\uff0c\u90a3\u4e48\u5e94\u8be5\u662f\uff1a<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A|B) \\gt P(A).<\/span>\u5728\u8fd9\u91cc\uff0c<span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u589e\u5f3a\u4e86 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span>\uff0c\u56e0\u6b64\u6211\u4eec\u8bf4\u8fd9\u4e24\u4e2a\u4e8b\u4ef6\u4e4b\u95f4\u6709<strong>\u6b63\u5173\u8054<\/strong>\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u53cd\u4e4b\uff0c\u5982\u679c\u5403\u7cd6\u679c\u53ef\u4ee5\u9884\u9632\u9f8b\u9f7f\uff0c\u90a3\u4e48\u5e94\u8be5\u662f\uff1a<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A|B) \\lt P(A).<\/span>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c<span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u6291\u5236\u4e86 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span>\uff0c\u56e0\u6b64\u6211\u4eec\u8bf4\u8fd9\u4e24\u4e2a\u4e8b\u4ef6\u4e4b\u95f4\u6709<strong>\u8d1f\u5173\u8054<\/strong>\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5982\u679c\u8fd9\u4e24\u4e2a\u4e8b\u4ef6\u4e4b\u95f4\u6ca1\u6709\u4efb\u4f55\u5173\u7cfb\uff0c\u65e0\u8bba\u662f\u6b63\u5173\u8054\u8fd8\u662f\u8d1f\u5173\u8054\uff0c\u90a3\u4e48\u5e94\u8be5\u662f\uff1a<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A|B) = P(A).<\/span>\u4ece\u8fd9\u91cc\u53ef\u4ee5\u63a8\u65ad\uff0c\u5927\u591a\u6570\u6982\u7387\u4e66\u7c4d\u4e2d\u5c06\u5176\u4f5c\u4e3a\u5b9a\u4e49\uff1a<\/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;\">\u8fd9\u4e2a\u63a8\u7406\u663e\u793a\u4e86\u6761\u4ef6\u6982\u7387\u4e0e\u4e8b\u4ef6\u72ec\u7acb\u6027\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #800000;\"><strong>\u5b9a\u4e49\uff1a<\/strong><\/span> \u7ed9\u5b9a\u4e24\u4e2a\u4e8b\u4ef6 <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span>\uff0c\u5982\u679c\u5b83\u4eec\u6ee1\u8db3\u4ee5\u4e0b\u5173\u7cfb\uff0c\u5219\u79f0\u5b83\u4eec\u662f<strong>\u72ec\u7acb\u7684<\/strong>\uff1a<\/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>\u4e8b\u4ef6\u72ec\u7acb\u6027\u4e0e\u4e8b\u4ef6\u8865\u96c6\u7684\u72ec\u7acb\u6027<\/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;\">\u4e24\u4e2a\u4e8b\u4ef6<\/span><\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u7684\u72ec\u7acb\u6027\u88ab\u8bc1\u660e\u7b49\u4ef7\u4e8e <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u4e0e <span class=\"katex-eq\" data-katex-display=\"false\">B^c<\/span> \u7684\u72ec\u7acb\u6027\uff0c <span class=\"katex-eq\" data-katex-display=\"false\">A^c<\/span> \u4e0e <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u7684\u72ec\u7acb\u6027\uff0c\u4ee5\u53ca <span class=\"katex-eq\" data-katex-display=\"false\">A^c<\/span> \u4e0e <span class=\"katex-eq\" data-katex-display=\"false\">B^c<\/span> \u7684\u72ec\u7acb\u6027\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #000080;\"><strong>\u8bc1\u660e<\/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>; \u5047\u8bbe<\/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>; \u56e0\u4e3a <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\">\u53c2\u89c1\u7ec3\u4e602\u7684\u53d1\u5c55<\/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>; \u4ece (2) \u548c (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>; \u4ece (1) \u548c (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>; \u56e0 <span class=\"katex-eq\" data-katex-display=\"false\">P(A)<\/span> \u56e0\u5f0f\u5206\u89e3<\/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\">\u53c2\u89c1\u7ec3\u4e601\u7684\u53d1\u5c55<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u8fd9\u6700\u540e\u4e00\u4e2a\u8868\u8fbe\u5f0f\u8bfb\u4f5c\uff1a\u201c\u4ece <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u72ec\u7acb\u7684\u4e8b\u5b9e\u53ef\u4ee5\u63a8\u65ad\u51fa <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">B^c<\/span> \u4e5f\u662f\u72ec\u7acb\u7684\u3002\u201d<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u9006\u5411\u8bc1\u660e\u4e5f\u662f\u4ee5\u7c7b\u4f3c\u7684\u65b9\u5f0f\u8fdb\u884c\u7684\u3002<\/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>; \u5047\u8bbe<\/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\">\u53c2\u89c1\u7ec3\u4e601\u7684\u53d1\u5c55<\/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>; \u5728\u53f3\u8fb9\u6267\u884c\u62ec\u53f7\u4e2d\u7684\u4e58\u79ef\u3002<\/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>; \u56e0\u4e3a <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\">\u53c2\u89c1\u7ec3\u4e602\u7684\u53d1\u5c55<\/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>; \u4ece (1)\uff0c(2) \u548c (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>; \u6d88\u9664\u76f8\u4f3c\u9879<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify; color: #000000;\">\u8fd9\u8868\u8fbe\u4e3a\uff1a\u201c\u4ece <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">B^c<\/span> \u72ec\u7acb\u7684\u4e8b\u5b9e\u53ef\u4ee5\u63a8\u65ad\u51fa <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u548c <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u4e5f\u662f\u72ec\u7acb\u7684\u3002\u201d<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u6700\u540e\uff0c\u4ece\u8fd9\u4e24\u4e2a\u63a8\u7406\u4e2d\u5f97\u51fa <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u4e0e <span class=\"katex-eq\" data-katex-display=\"false\">B<\/span> \u72ec\u7acb\u6027\u548c <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> \u4e0e <span class=\"katex-eq\" data-katex-display=\"false\">B^c<\/span> \u72ec\u7acb\u6027\u4e4b\u95f4\u7684\u7b49\u4ef7\u5173\u7cfb\u5df2\u88ab\u8bc1\u660e\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\">\u5176\u4ed6\u88ab\u8bc1\u660e\u7684\u7b49\u4ef7\u5173\u7cfb\u53ef\u4ee5\u7528\u7c7b\u4f3c\u65b9\u5f0f\u83b7\u5f97\u3002\u8fd9\u4e9b\u5c06\u4f5c\u4e3a\u8bfb\u8005\u7684\u6311\u6218 &gt;:D<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6761\u4ef6\u6982\u7387\u4e0e\u4e8b\u4ef6\u72ec\u7acb\u6027 \u6458\u8981\u5728\u672c\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u5c06\u63a2\u8ba8\u6761\u4ef6\u6982\u7387\u7684\u6982\u5ff5\u4ee5\u53ca\u4e8b\u4ef6\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u3002\u6211\u4eec\u5c06\u5b66\u4e60\u5982\u4f55\u8ba1\u7b97\u6761\u4ef6\u6982\u7387\u5e76\u786e\u5b9a\u4e8b\u4ef6\u4e4b\u95f4\u7684\u4f9d\u8d56\u6027\u6216\u72ec\u7acb\u6027\u3002\u6211\u4eec\u5c06\u901a\u8fc7\u5b9e\u9645\u4f8b\u5b50\uff0c\u5982\u7814\u7a76\u7cd6\u679c\u6d88\u8d39\u8005\u4e2d\u9f8b\u9f7f\u7684\u60a3\u75c5\u7387\uff0c\u6765\u8bf4\u660e\u8fd9\u4e9b\u6982\u5ff5\u3002\u6700\u540e\uff0c\u4f60\u5c06\u6e05\u695a\u5730\u7406\u89e3\u5982\u4f55\u5e94\u7528\u6761\u4ef6\u6982\u7387\u5e76\u5206\u6790\u4f9d\u8d56\u548c\u72ec\u7acb\u4e8b\u4ef6\u3002 \u5b66\u4e60\u76ee\u6807\uff1a \u5728\u672c\u8282\u8bfe\u7ed3\u675f\u65f6\uff0c\u4f60\u5c06\u80fd\u591f\uff1a \u7406\u89e3\u6761\u4ef6\u6982\u7387\u7684\u5b9a\u4e49\u53ca\u5176\u4e0e\u4e8b\u4ef6\u4ea4\u96c6\u548c\u4e2a\u4f53\u6982\u7387\u7684\u5173\u7cfb\u3002 \u8bc6\u522b\u901a\u8fc7\u6bd4\u8f83\u6761\u4ef6\u6982\u7387\u786e\u5b9a\u4e8b\u4ef6\u4e4b\u95f4\u7684\u6b63\u8d1f\u5173\u8054\u3002 \u68c0\u9a8c\u4e0d\u540c\u4e8b\u4ef6\u4e4b\u95f4\u7684\u72ec\u7acb\u6027\u3002 \u5185\u5bb9\u7d22\u5f15 \u6761\u4ef6\u6982\u7387 \u6761\u4ef6\u6982\u7387\u7684\u6b63\u5f0f\u5b9a\u4e49 \u4e8b\u4ef6\u4e4b\u95f4\u7684\u5173\u7cfb \u4e8b\u4ef6\u72ec\u7acb\u6027\u4e0e\u4e8b\u4ef6\u8865\u96c6\u7684\u72ec\u7acb\u6027 \u6761\u4ef6\u6982\u7387 \u4e8b\u4ef6A\u5728\u4e8b\u4ef6B\u5df2\u7ecf\u53d1\u751f\u7684\u60c5\u51b5\u4e0b\u53d1\u751f\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f\u8fd9\u79cd\u6982\u7387\u7684\u8ba1\u7b97\u6d89\u53ca\u6761\u4ef6\u6982\u7387\u7684\u6982\u5ff5\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u5c06\u7814\u7a76\u6761\u4ef6\u6982\u7387\u3001\u5176\u5b9a\u4e49\u4ee5\u53ca\u5982\u4f55\u4ece\u4e2d\u63a8\u65ad\u4e8b\u4ef6\u4e4b\u95f4\u7684\u4f9d\u8d56\u6027\u548c\u72ec\u7acb\u6027\u5173\u7cfb\u3002 \u5047\u8bbe\u6211\u4eec\u60f3\u8981\u6d4b\u91cf\u5e38\u89c4\u7cd6\u679c\u6d88\u8d39\u8005\u4e2d\u9f8b\u9f7f\u7684\u60a3\u75c5\u7387\u3002\u5982\u679c\u6211\u4eec\u68c0\u67e5\u4e00\u4e2a\u7531\u4e2a\u4eba\u7ec4\u6210\u7684\u6837\u672c\u7a7a\u95f4\u6211\u4eec\u4f1a\u770b\u5230\u5b83\u53ef\u4ee5\u5206\u62104\u4e2a\u5b50\u96c6\uff1a \u7531\u6b64\u53ef\u77e5\uff0c \u548c \u4f46 \u4e0d\u4e00\u5b9a\u4e3a\u7a7a\u3002\u4e00\u822c\u60c5\u51b5\u4e0b\u5982\u56fe\u6240\u793a\uff1a \u90a3\u4e48\uff0c\u5982\u679c\u6211\u4eec\u8bb0\u4f4f\u6982\u7387\u7684\u5b9a\u4e49\u4e3a\u76f8\u5bf9\u9891\u7387\u7684\u6781\u9650\uff0c\u6211\u4eec\u53ef\u4ee5\u8bf4\u4e00\u4e2a\u4eba\u5728\u5df2\u7ecf\u786e\u8ba4\u5176\u5403\u7cd6\u679c\u7684\u60c5\u51b5\u4e0b\u6709\u9f8b\u9f7f\u7684\u6982\u7387 \u5c06\u662f\uff1a \u53e6\u4e00\u65b9\u9762\uff0c\u6709\uff1a \u21b3 &nbsp; 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