{"id":26727,"date":"2021-04-21T13:00:36","date_gmt":"2021-04-21T13:00:36","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=26727"},"modified":"2024-05-21T21:48:35","modified_gmt":"2024-05-21T21:48:35","slug":"%e8%b4%9d%e5%8f%b6%e6%96%af%e5%ae%9a%e7%90%86%e4%b8%8e%e5%a4%8d%e5%90%88%e6%a6%82%e7%8e%87","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/zh\/%e8%b4%9d%e5%8f%b6%e6%96%af%e5%ae%9a%e7%90%86%e4%b8%8e%e5%a4%8d%e5%90%88%e6%a6%82%e7%8e%87\/","title":{"rendered":"\u8d1d\u53f6\u65af\u5b9a\u7406\u4e0e\u590d\u5408\u6982\u7387"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>\u8d1d\u53f6\u65af\u5b9a\u7406\u4e0e\u590d\u5408\u6982\u7387<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>\u6458\u8981<\/strong><br \/><em>\u5728\u672c\u8282\u8bfe\u4e2d\uff0c\u6211\u4eec\u8ba8\u8bba\u4e86\u6982\u7387\u7684\u4e24\u4e2a\u57fa\u672c\u6982\u5ff5\uff1a\u6761\u4ef6\u6982\u7387\u548c\u590d\u5408\u6982\u7387\u3002\u5f3a\u8c03\u4e86<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>\u4e4b\u95f4\u7684\u533a\u522b\u3002\u590d\u5408\u6982\u7387\u5b9a\u7406\u6307\u51fa\uff0c\u4e8b\u4ef6<span class=\"katex-eq\" data-katex-display=\"false\">A<\/span>\u7684\u6982\u7387\u53ef\u4ee5\u8868\u793a\u4e3a\u6761\u4ef6\u6982\u7387<span class=\"katex-eq\" data-katex-display=\"false\">P(A|B_i)<\/span>\u4e58\u4ee5\u4e8b\u4ef6<span class=\"katex-eq\" data-katex-display=\"false\">B_i<\/span>\u7684\u6982\u7387\u7684\u603b\u548c\u3002\u968f\u540e\uff0c\u6211\u4eec\u4ecb\u7ecd\u4e86\u8d1d\u53f6\u65af\u5b9a\u7406\uff0c\u5b83\u5141\u8bb8\u4f7f\u7528\u6761\u4ef6\u6982\u7387<span class=\"katex-eq\" data-katex-display=\"false\">P(A|B_k)<\/span>\u3001\u6982\u7387<span class=\"katex-eq\" data-katex-display=\"false\">P(B_k)<\/span>\u548c\u6761\u4ef6\u6982\u7387<span class=\"katex-eq\" data-katex-display=\"false\">P(A|B_i)<\/span>\u4e58\u4ee5\u4e8b\u4ef6<span class=\"katex-eq\" data-katex-display=\"false\">B_i<\/span>\u7684\u6982\u7387\u7684\u603b\u548c\u6765\u8ba1\u7b97\u6761\u4ef6\u6982\u7387<span class=\"katex-eq\" data-katex-display=\"false\">P(B_k|A)<\/span>\u3002\u8fd9\u4e9b\u6982\u5ff5\u5bf9\u4e8e\u7406\u89e3\u548c\u5e94\u7528\u5404\u79cd\u4e0a\u4e0b\u6587\u4e2d\u7684\u6761\u4ef6\u6982\u7387\u662f\u81f3\u5173\u91cd\u8981\u7684\uff0c\u800c\u8d1d\u53f6\u65af\u5b9a\u7406\u63d0\u4f9b\u4e86\u4e00\u79cd\u5f3a\u5927\u7684\u5de5\u5177\uff0c\u53ef\u4ee5\u6839\u636e\u65b0\u4fe1\u606f\u66f4\u65b0\u6982\u7387\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\u5b66\u751f\u5c06\u80fd\u591f\uff1a\n<\/p>\n<ol>\n<li><strong>\u7406\u89e3<\/strong>\u6761\u4ef6\u6982\u7387\u7684\u6982\u5ff5\uff0c\u5e76\u533a\u5206<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>\u3002<\/li>\n<li><strong>\u8ba1\u7b97<\/strong>\u4f7f\u7528\u590d\u5408\u6982\u7387\u7684\u4e8b\u4ef6\u6982\u7387\u3002<\/li>\n<li><strong>\u6f14\u793a<\/strong>\u8d1d\u53f6\u65af\u89c4\u5219\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>\u5185\u5bb9\u76ee\u5f55<\/u><\/strong><br \/>\n<a href=\"#1\">\u590d\u5408\u6982\u7387\u4e0e\u6761\u4ef6\u6982\u7387<\/a><br \/>\n<a href=\"#2\">\u8d1d\u53f6\u65af\u5b9a\u7406<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/BDUTXmxlsM0\" 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 style=\"text-align: justify; color: #000000;\">\u5728<a href=\"https:\/\/toposuranos.com\/probabilidad-condicional-e-independencia-entre-eventos\/\" rel=\"noopener\" target=\"_blank\">\u4e0a\u4e00\u8282\u8bfe<\/a>\u4e2d\uff0c\u6211\u4eec\u56de\u987e\u4e86\u6761\u4ef6\u6982\u7387\u7684\u6982\u5ff5\uff0c\u5e76\u6f84\u6e05\u4e86\u4e0d\u5e94\u5c06\u5f62\u5f0f\u4e3a<span class=\"katex-eq\" data-katex-display=\"false\">P(A|B)<\/span>\u7684\u6761\u4ef6\u6982\u7387\u4e0e<span class=\"katex-eq\" data-katex-display=\"false\">P(B|A)<\/span>\u6df7\u6dc6\u3002\u5c3d\u7ba1\u5728\u65e5\u5e38\u8bed\u8a00\u4e2d\u6761\u4ef6\u6027\u53ef\u80fd\u4ee4\u4eba\u56f0\u60d1\uff0c\u4f46\u5728\u6570\u5b66\u4e0a\u5b83\u4eec\u662f\u5b8c\u5168\u4e0d\u540c\u7684\u4e24\u4e2a\u6982\u5ff5\uff0c\u4f46\u5374\u662f\u76f8\u5173\u7684\u3002\u8fd9\u79cd\u5173\u7cfb\u7531\u8d1d\u53f6\u65af\u5b9a\u7406\u63cf\u8ff0\uff0c\u8d1d\u53f6\u65af\u5b9a\u7406\u57fa\u4e8e\u590d\u5408\u6982\u7387\u7684\u6982\u5ff5\u8fdb\u884c\u516c\u5f0f\u5316\u3002<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u590d\u5408\u6982\u7387\u4e0e\u6761\u4ef6\u6982\u7387<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #800000;\">\u5b9a\u7406\uff1a<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=BDUTXmxlsM0&amp;t=210s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u5982\u679c<span class=\"katex-eq\" data-katex-display=\"false\">A<\/span>\u662f\u4e00\u4e2a\u4e8b\u4ef6<\/span><\/strong><\/a>\uff0c\u4e14<span class=\"katex-eq\" data-katex-display=\"false\">B_1, B_2, \\cdots, B_n<\/span>\u6784\u6210\u4e00\u7ec4\u4e92\u65a5\u4e8b\u4ef6\uff0c\u90a3\u4e48<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\bigcup_{i=1}^n B_i = \\Omega,<\/span>\u5219\u6709\uff1a<\/p>\n<p style=\"text-align: center; color: #000000; background-color: #A0FFA0;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{P(A) = \\displaystyle \\sum_{i=1}^n P(A|B_i) P(B_i)}<\/span>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=BDUTXmxlsM0&amp;t=428s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u8fd9\u79cd\u8868\u793a\u4e8b\u4ef6<span class=\"katex-eq\" data-katex-display=\"false\">A<\/span>\u7684\u6982\u7387\u7684\u65b9\u5f0f<\/span> <\/strong><\/a>\u6211\u4eec\u79f0\u4e4b\u4e3a<strong><span class=\"katex-eq\" data-katex-display=\"false\">A<\/span>\u7684\u590d\u5408\u6982\u7387<\/strong>\u3002<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #800000;\">\u8bc1\u660e\uff1a<\/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\">A<\/span>\u662f\u4e00\u4e2a\u4e8b\u4ef6<\/td>\n<td>; \u524d\u63d0<\/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\">\\displaystyle \\bigcup_{i=1}^n B_i = \\Omega<\/span><\/td>\n<td>; \u524d\u63d0<\/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\">B_1, \\cdots, B_n<\/span>\u662f\u4e92\u65a5\u4e8b\u4ef6<\/td>\n<td>; \u524d\u63d0<\/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\">(A\\cap B_i)\\cap(A\\cap B_j) = \\varnothing,<\/span>\u5176\u4e2d<span class=\"katex-eq\" data-katex-display=\"false\">i\\neq j<\/span>\u4e14<span class=\"katex-eq\" data-katex-display=\"false\">i,j\\in \\{1,2,3,\\cdots n\\}<\/span><\/td>\n<td>; \u7531(1,2,3)<\/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\">\\displaystyle \\bigcup_{i=1}^n \\left(A \\cap B_i \\right) = A<\/span><\/td>\n<td>; \u7531(1,2,3)<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(6)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle P(A) = P\\left( \\bigcup_{i=1}^n \\left(A \\cap B_i \\right) \\right) = \\sum_{i=1}^n P\\left( A \\cap B_i \\right)<\/span><\/td>\n<td>; \u7531(4,5)<\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(7)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> P(A|B_i) = \\dfrac{P(A\\cap B_i)}{P(B_i)}<\/span><\/td>\n<td>; \u6761\u4ef6\u6982\u7387\u7684\u5b9a\u4e49<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\"> P(A\\cap B_i) = P(A|B_i) P(B_i)<\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">(8)<\/span><\/td>\n<td><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{\\displaystyle P(A) = \\sum_{i=1}^n P(A|B_i) P(B_i)}<\/span><\/td>\n<td>; \u7531(6,7)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u8d1d\u53f6\u65af\u5b9a\u7406<\/h2>\n<p style=\"text-align: justify; color: #000000;\"><a href=\"https:\/\/www.youtube.com\/watch?v=BDUTXmxlsM0&amp;t=801s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u5728\u4e0e\u524d\u8ff0\u5b9a\u7406\u76f8\u540c\u7684\u4e0a\u4e0b\u6587\u4e2d<\/span><\/strong><\/a>\uff0c\u6211\u4eec\u6709\u5982\u4e0b\u5b9a\u7406\uff1a<\/p>\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #800000;\">\u5b9a\u7406\uff1a<\/span><\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\"> P(B_k|A) = \\dfrac{P(A|B_k)P(B_k)}{\\displaystyle\\sum_{i=1}^n P(A|B_i)P(B_i)} = \\dfrac{P(A|B_k)P(B_k)}{P(A)}<\/span>\n<p style=\"text-align: justify; color: #000000;\"><span style=\"color: #800000;\">\u8bc1\u660e\uff1a<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=BDUTXmxlsM0&amp;t=855s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u5982\u679c<span class=\"katex-eq\" data-katex-display=\"false\">A<\/span>\u662f\u4e00\u4e2a\u4efb\u610f\u4e8b\u4ef6<\/span><\/strong><\/a>\u4e14<span class=\"katex-eq\" data-katex-display=\"false\">B_1, B_2, \\cdots, B_n<\/span>\u662f\u4e00\u7ec4\u4e92\u65a5\u4e8b\u4ef6\uff0c\u90a3\u4e48<span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\bigcup_{i=1}^n B_i = \\Omega,<\/span>\u7531\u524d\u8ff0\u590d\u5408\u6982\u7387\u5b9a\u7406\uff0c\u6211\u4eec\u6709\uff1a<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A) = \\displaystyle \\sum_{i=1}^n P(A|B_i)P(B_i)<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u73b0\u5728\uff0c\u5229\u7528<span class=\"katex-eq\" data-katex-display=\"false\">P(X\\cap Y) = P(X|Y)P(Y),<\/span>\u5982\u679c\u6211\u4eec\u5c06<span class=\"katex-eq\" data-katex-display=\"false\">Y=A<\/span>\u548c<span class=\"katex-eq\" data-katex-display=\"false\">X=B_k<\/span>\u4ee3\u5165\uff0c\u6211\u4eec\u5c06\u5f97\u5230<\/p>\n<p style=\"text-align: center; color: #000000; background-color: #b0b0ff;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A) = \\dfrac{P(B_k \\cap A)}{P(B_k|A)}<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u53e6\u4e00\u65b9\u9762\uff0c\u6211\u4eec\u6709<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A|B_k) = \\dfrac{P(A\\cap B_k)}{P(B_k)}<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u7531\u6b64\u53ef\u5f97<\/p>\n<p style=\"text-align: center; color: #000000; background-color: #b0ffb0;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(B_k \\cap A) = P(A|B_k)P(B_k)<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u73b0\u5728\uff0c\u5982\u679c\u6211\u4eec\u5c06\u7eff\u8272\u90e8\u5206\u4ee3\u5165\u84dd\u8272\u90e8\u5206\uff0c\u6211\u4eec\u5c06\u5f97\u5230<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">P(A) = \\dfrac{P(A|B_k)P(B_k)}{P(B_k|A)}<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u8fd9\u76f8\u5f53\u4e8e\u8bf4<\/p>\n<p style=\"text-align: center; color: #000000;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{P(B_k|A) = \\dfrac{P(A|B_k)P(B_k)}{P(A)}= \\dfrac{P(A|B_k)P(B_k)}{\\displaystyle \\sum_{i=1}^n P(A|B_i) P(B_i)} }<\/span>\n<p style=\"text-align: justify; color: #000000;\">\u8fd9\u5c31\u662f\u6211\u4eec\u8981\u8bc1\u660e\u7684\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8d1d\u53f6\u65af\u5b9a\u7406\u4e0e\u590d\u5408\u6982\u7387 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