{"id":379,"date":"2023-08-01T12:09:39","date_gmt":"2023-08-01T12:09:39","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e8%b4%9d%e5%8f%b6%e6%96%af%e5%ae%9a%e7%90%86\/"},"modified":"2023-08-01T12:09:39","modified_gmt":"2023-08-01T12:09:39","slug":"%e8%b4%9d%e5%8f%b6%e6%96%af%e5%ae%9a%e7%90%86","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e8%b4%9d%e5%8f%b6%e6%96%af%e5%ae%9a%e7%90%86\/","title":{"rendered":"\u8d1d\u53f6\u65af\u5b9a\u7406"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f\u8d1d\u53f6\u65af\u5b9a\u7406\u4ee5\u53ca\u5b83\u5728\u6982\u7387\u548c\u7edf\u8ba1\u4e2d\u7684\u7528\u9014\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u4e86\u89e3\u8d1d\u53f6\u65af\u5b9a\u7406\u7684\u516c\u5f0f\u662f\u4ec0\u4e48\u3001\u8d1d\u53f6\u65af\u5b9a\u7406\u7684\u89e3\u51b3\u793a\u4f8b\u4ee5\u53ca\u8be5\u5b9a\u7406\u7684\u5e94\u7528\u662f\u4ec0\u4e48\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-teorema-de-bayes\"><\/span>\u4ec0\u4e48\u662f\u8d1d\u53f6\u65af\u5b9a\u7406\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u6982\u7387\u8bba\u4e2d\uff0c<strong>\u8d1d\u53f6\u65af\u5b9a\u7406<\/strong>\u662f\u7528\u4e8e\u5728\u5df2\u77e5\u4e8b\u4ef6\u7684\u5148\u9a8c\u4fe1\u606f\u65f6\u8ba1\u7b97\u8be5\u4e8b\u4ef6\u7684\u6982\u7387\u7684\u5b9a\u5f8b\u3002<\/p>\n<p>\u66f4\u5177\u4f53\u5730\u8bf4\uff0c\u8d1d\u53f6\u65af\u5b9a\u7406\u5728\u6570\u5b66\u4e0a\u5c06\u7ed9\u5b9a\u4e8b\u4ef6 B \u7684\u4e8b\u4ef6 A \u7684\u6982\u7387\u4e0e\u7ed9\u5b9a A \u7684\u4e8b\u4ef6 B \u7684\u6982\u7387\u8054\u7cfb\u8d77\u6765\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u5982\u679c\u60a8\u4e8b\u5148\u77e5\u9053\u4e00\u4e2a\u4eba\u5728\u60a3\u6d41\u611f\u65f6\u4f1a\u5934\u75db\u7684\u6982\u7387\uff0c\u5219\u53ef\u4ee5\u4f7f\u7528\u8d1d\u53f6\u65af\u5b9a\u7406\u6765\u786e\u5b9a\u4e00\u4e2a\u4eba\u5728\u5934\u75db\u65f6\u60a3\u6d41\u611f\u7684\u6982\u7387\u3002<\/p>\n<p>\u8d1d\u53f6\u65af\u5b9a\u7406\u6709\u5f88\u591a\u5e94\u7528\uff0c\u4f8b\u5982\uff0c\u5b83\u5728\u533b\u5b66\u3001\u7ecf\u6d4e\u5b66\u6216\u6280\u672f\u4e2d\u7528\u4e8e\u8ba1\u7b97\u53d7\u5176\u4ed6\u4e8b\u4ef6\u5236\u7ea6\u7684\u67d0\u4e9b\u4e8b\u4ef6\u7684\u6982\u7387\u3002\u4e0b\u9762\uff0c\u6211\u4eec\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u8d1d\u53f6\u65af\u5b9a\u7406\u7684\u4e0d\u540c\u5e94\u7528\u3002<\/p>\n<p>\u8d1d\u53f6\u65af\u5b9a\u7406\u662f\u7531\u82f1\u56fd\u6570\u5b66\u5bb6\u6258\u9a6c\u65af\u00b7\u8d1d\u53f6\u65af\uff08Thomas Bayes\uff0c1702-1761\uff09\u53d1\u660e\u7684\uff0c\u5c3d\u7ba1\u8be5\u5b9a\u7406\u662f\u5728\u4ed6\u53bb\u4e16\u540e\u4e8e 1763 \u5e74\u51fa\u7248\u7684\u3002 <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u6761\u4ef6\u6761\u4ef6\u6982\u7387\/\">\u6761\u4ef6\u6982\u7387<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-teorema-de-bayes\"><\/span>\u8d1d\u53f6\u65af\u5b9a\u7406\u7684\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8d1d\u53f6\u65af\u5b9a\u7406\u6307\u51fa\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u7531\u4e00\u7ec4\u6982\u7387\u4e0d\u4e3a\u96f6<a href=\"https:\/\/statorials.org\/cn\/\u4e92\u65a5\u4e8b\u4ef6\/\">\u7684\u4e92\u65a5\u4e8b\u4ef6<\/a>{A <sub>1<\/sub> , A <sub>2<\/sub> ,\u2026, A <sub>i<\/sub> ,\u2026, A <sub>n<\/sub> } \u548c\u53e6\u4e00\u4e2a\u4e8b\u4ef6 B \u7ec4\u6210\u7684\u6837\u672c\u7a7a\u95f4\uff0c\u6211\u4eec\u53ef\u4ee5\u5728\u6570\u5b66\u4e0a\u5c06\u6761\u4ef6\u5173\u8054\u8d77\u6765\u7ed9\u5b9a\u4e8b\u4ef6 B \u65f6 A <sub>i<\/sub>\u7684\u6982\u7387\u4ee5\u53ca\u7ed9\u5b9a A <sub>i<\/sub>\u65f6 B \u7684\u6761\u4ef6\u6982\u7387\u3002<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u8d1d\u53f6\u65af\u5b9a\u7406<\/strong>\uff0c\u4e5f\u79f0\u4e3a<strong>\u8d1d\u53f6\u65af\u89c4\u5219<\/strong>\uff0c\u5176\u516c\u5f0f\u4e3a\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/theoreme-de-bayes.png\" alt=\"\u8d1d\u53f6\u65af\u5b9a\u7406\u7684\u516c\u5f0f\u3001\u8d1d\u53f6\u65af\u89c4\u5219\" class=\"wp-image-8514\" width=\"370\" height=\"318\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p style=\"margin-bottom:7px\">\u91d1\u5b50\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:8px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-62ffcdb184381914ec23155ad31bbfb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A_i|B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u662f\u4e8b\u4ef6 A <sub>i<\/sub>\u7ed9\u5b9a\u4e8b\u4ef6 B \u7684\u6761\u4ef6\u6982\u7387\uff0c\u79f0\u4e3a\u540e\u9a8c\u6982\u7387\u3002<\/li>\n<li style=\"margin-bottom:8px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-676b61239ea67554603513360fbea72b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(B|A_i)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u662f\u7ed9\u5b9a\u4e8b\u4ef6 A <sub>i<\/sub>\u65f6\u4e8b\u4ef6 B \u7684\u6761\u4ef6\u6982\u7387\u3002<\/li>\n<li style=\"margin-bottom:8px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-be31252343b496b792bee3e55a99979f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A_i)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"46\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u662f\u4e8b\u4ef6 A <sub>i<\/sub>\u53d1\u751f\u7684\u6982\u7387\uff0c\u79f0\u4e3a\u5148\u9a8c\u6982\u7387\u3002<\/li>\n<\/ul>\n<p>\u8bf7\u6ce8\u610f\uff0c\u8d1d\u53f6\u65af\u5b9a\u7406\u516c\u5f0f\u7684\u5206\u6bcd\u662f\u4e8b\u4ef6 B \u7684<a href=\"https:\/\/statorials.org\/cn\/\u5168\u6982\u7387\u5b9a\u7406\/\">\u603b\u6982\u7387<\/a>\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-teorema-de-bayes\"><\/span>\u8d1d\u53f6\u65af\u5b9a\u7406\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u8d1d\u53f6\u65af\u5b9a\u7406\u7684\u5b9a\u4e49\u53ca\u5176\u516c\u5f0f\u662f\u4ec0\u4e48\uff0c\u6211\u4eec\u5c06\u770b\u5230\u4e00\u4e2a\u5df2\u89e3\u51b3\u7684\u793a\u4f8b\uff0c\u8bf4\u660e\u5982\u4f55\u4f7f\u7528\u8d1d\u53f6\u65af\u5b9a\u7406\u8ba1\u7b97\u6982\u7387\uff0c\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u8be5\u6982\u5ff5\u3002<\/p>\n<ul>\n<li>\u4e00\u5bb6\u7535\u5b50\u5546\u5e97\u9500\u552e\u4e09\u4e2a\u54c1\u724c\u7684\u7535\u89c6\uff1aX\u3001Y\u3001Z\u3002\u4f30\u8ba1\u9500\u552e\u989d\u7684 20% \u662f\u6709\u7f3a\u9677\u7684\u54c1\u724c\u7535\u89c6\uff0c3% \u7684 Y \u54c1\u724c\u7535\u89c6\u6709\u7f3a\u9677\uff0c4% \u7684 Z \u54c1\u724c\u7535\u89c6\u6709\u7f3a\u9677\u3002\u7ed9\u5b9a\u4e00\u53f0\u6709\u7f3a\u9677\u7684\u7535\u89c6\uff0c\u5b83\u662f Z \u54c1\u724c\u7535\u89c6\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f<\/li>\n<\/ul>\n<p>\u8be5\u7ec3\u4e60\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u5ba2\u6237\u8d2d\u4e70\u6bcf\u4e2a\u54c1\u724c\u7535\u89c6\u7684\u6982\u7387\uff1a<\/p>\n<ul>\n<li>\u4e8b\u4ef6 A <sub>1<\/sub> \uff1a\u987e\u5ba2\u8d2d\u4e70 X \u54c1\u724c\u7535\u89c6 \u2192 P(A <sub>1<\/sub> )=0.20<\/li>\n<li>\u4e8b\u4ef6 A <sub>2<\/sub> \uff1a\u987e\u5ba2\u8d2d\u4e70 Y \u54c1\u724c\u7535\u89c6 \u2192 P(A <sub>2<\/sub> )=0.50<\/li>\n<li>\u4e8b\u4ef6 A <sub>3<\/sub> \uff1a\u987e\u5ba2\u8d2d\u4e70 Z \u54c1\u724c\u7535\u89c6 \u2192 P(A <sub>3<\/sub> )=0.30<\/li>\n<\/ul>\n<p>\u6b64\u5916\uff0c\u8bfb\u6570\u8fd8\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u6bcf\u4e2a\u54c1\u724c\u7684\u7535\u89c6\u6709\u7f3a\u9677\u7684\u6982\u7387\uff1a<\/p>\n<p class=\"has-text-align-center\">\u4e8b\u4ef6B\uff1a\u7535\u89c6\u6545\u969c<\/p>\n<ul>\n<li>B|A <sub>1<\/sub> \uff1a\u7ed9\u5b9a\u4e00\u53f0\u54c1\u724c X \u7535\u89c6\uff0c\u8be5\u7535\u89c6\u6709\u7f3a\u9677 \u2192 P(B|A <sub>1<\/sub> )=0.05<\/li>\n<li> B|A <sub>2<\/sub> \uff1a\u7ed9\u5b9a\u4e00\u53f0 Y \u54c1\u724c\u7535\u89c6\uff0c\u8be5\u7535\u89c6\u6709\u7f3a\u9677 \u2192 P(B|A <sub>2<\/sub> )=0.03<\/li>\n<li> B|A <sub>3<\/sub> \uff1a\u7ed9\u5b9a\u4e00\u53f0 Z \u54c1\u724c\u7535\u89c6\uff0c\u8be5\u7535\u89c6\u6709\u7f3a\u9677 \u2192 P(B|A <sub>3<\/sub> )=0.04<\/li>\n<\/ul>\n<p>\u6240\u4ee5\u6211\u4eec\u611f\u5174\u8da3\u7684\u6240\u6709\u4e8b\u4ef6\u7684<a href=\"https:\/\/statorials.org\/cn\/\u6811\u5f62\u56fe\/\">\u6982\u7387\u6811<\/a>\u5982\u4e0b\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"370\" height=\"257\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/theoreme-de-probabilite-de-bayes.png\" alt=\"\u8d1d\u53f6\u65af\u5b9a\u7406\u6811\u56fe\" class=\"wp-image-8525\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u56e0\u6b64\uff0c\u8981\u8ba1\u7b97\u7ed9\u5b9a\u4e00\u53f0\u6709\u7f3a\u9677\u7684\u7535\u89c6\u673a\u4e3a\u54c1\u724c Z \u7684\u6982\u7387\uff0c\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u8d1d\u53f6\u65af\u5b9a\u7406\u4e2d\u7684\u516c\u5f0f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c15e369635dcf17952b5d832a818d535_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A_i|B)=\\cfrac{P(B|A_i)\\cdot P(A_i)}{\\displaystyle \\sum_{k=1}^n P(B|A_k)\\cdot P(A_k)}\" title=\"Rendered by QuickLaTeX.com\" height=\"77\" width=\"251\" style=\"vertical-align: -49px;\"><\/p>\n<\/p>\n<p>\u4f7f\u7528\u672c\u4f8b\u4e2d\u4f7f\u7528\u7684\u672f\u8bed\uff0c\u8d1d\u53f6\u65af\u516c\u5f0f\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7c2b74ac3ed5173c4a40837675d8282d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A_3|B)=\\cfrac{P(B|A_3)\\cdot P(A_3)}{P(B|A_1)\\cdot P(A_1)+P(B|A_2)\\cdot P(A_2)+ P(B|A_3)\\cdot P(A_3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"525\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u7ed9\u5b9a\u7684\u6709\u7f3a\u9677\u7535\u89c6\u662f\u54c1\u724c Z \u7684\u6982\u7387\u7684\u8ba1\u7b97\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-818d0f3336f855a1315d6a94f01d1876_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(A_3|B)&amp;=\\cfrac{P(B|A_3)\\cdot P(A_3)}{P(B|A_1)\\cdot P(A_1)+P(B|A_2)\\cdot P(A_2)+ P(B|A_3)\\cdot P(A_3)}\\\\[2ex]&amp;=\\cfrac{0,04\\cdot 0,30}{0,05\\cdot 0,20+0,03\\cdot 0,50+0,04\\cdot 0,30}\\\\[2ex]&amp;=0,32\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"151\" width=\"525\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u7efc\u4e0a\u6240\u8ff0\uff0c\u5982\u679c\u4e00\u53f0\u7535\u89c6\u673a\u6709\u7f3a\u9677\uff0c\u5176\u5c5e\u4e8e Z \u54c1\u724c\u7684\u6982\u7387\u4e3a 32%\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"aplicaciones-del-teorema-de-bayes\"><\/span>\u8d1d\u53f6\u65af\u5b9a\u7406\u7684\u5e94\u7528<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8d1d\u53f6\u65af\u5b9a\u7406\u6709\u5f88\u591a\u5e94\u7528\uff0c\u5305\u62ec\uff1a<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u533b\u5b66\u6d4b\u8bd5<\/strong>\uff1a\u8d1d\u53f6\u65af\u5b9a\u7406\u5728\u533b\u5b66\u4e2d\u7ecf\u5e38\u7528\u4e8e\u786e\u5b9a\u901a\u8fc7\u8bca\u65ad\u6d4b\u8bd5\u7684\u6982\u7387\u3002\u4f8b\u5982\uff0c\u5728\u827e\u6ecb\u75c5\u6bd2\u68c0\u6d4b\u4e2d\uff0c\u5982\u679c\u68c0\u6d4b\u7ed3\u679c\u5448\u9633\u6027\uff0c\u8be5\u5b9a\u7406\u53ef\u7528\u4e8e\u8ba1\u7b97\u4e00\u4e2a\u4eba\u5b9e\u9645\u611f\u67d3\u75c5\u6bd2\u7684\u6982\u7387\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u8d22\u52a1\u5206\u6790<\/strong>\uff1a\u5728\u91d1\u878d\u9886\u57df\uff0c\u8d1d\u53f6\u65af\u5b9a\u7406\u7528\u4e8e\u8ba1\u7b97\u5728\u7ed9\u5b9a\u4e00\u7ec4\u7ecf\u6d4e\u53d8\u91cf\u7684\u60c5\u51b5\u4e0b\u53d1\u751f\u67d0\u4e9b\u7ecf\u6d4e\u4e8b\u4ef6\uff08\u4f8b\u5982\u80a1\u7968\u4ef7\u503c\u589e\u52a0\u6216\u51cf\u5c11\uff09\u7684\u6982\u7387\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u5e02\u573a\u7814\u7a76<\/strong>\uff1a\u8d1d\u53f6\u65af\u5b9a\u7406\u53ef\u4ee5\u786e\u5b9a\uff0c\u4f8b\u5982\uff0c\u4e00\u4e2a\u4eba\u5728\u770b\u5230\u8be5\u4ea7\u54c1\u7684\u5e7f\u544a\u540e\u8d2d\u4e70\u8be5\u4ea7\u54c1\u7684\u6982\u7387\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u5929\u6c14\u9884\u62a5<\/strong>\uff1a\u5929\u6c14\u6a21\u578b\u8fd8\u4f7f\u7528\u8d1d\u53f6\u65af\u5b9a\u7406\u6765\u786e\u5b9a\u57fa\u4e8e\u89c2\u6d4b\u6570\u636e\u7684\u7ed9\u5b9a\u5929\u6c14\u9884\u62a5\u5b9e\u73b0\u7684\u6982\u7387\u3002\u8fd9\u63d0\u9ad8\u4e86\u6c14\u5019\u9884\u62a5\u7684\u51c6\u786e\u6027\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u8ba1\u7b97\u673a\u5b89\u5168<\/strong>\u2013 \u5728\u7f51\u7edc\u5b89\u5168\u4e2d\uff0c\u53ef\u4ee5\u5e94\u7528\u8d1d\u53f6\u65af\u5b9a\u7406\u6765\u786e\u5b9a\u53ef\u7591\u6d3b\u52a8\u786e\u5b9e\u662f\u5bf9\u8ba1\u7b97\u673a\u7cfb\u7edf\u7684\u653b\u51fb\u7684\u53ef\u80fd\u6027\u3002<\/span> <\/li>\n<\/ol>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-del-teorema-de-bayes\"><\/span>\u89e3\u51b3\u8d1d\u53f6\u65af\u5b9a\u7406\u95ee\u9898<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u636e\u4f30\u8ba1\uff0c1%\u7684\u4eba\u53e3\u60a3\u6709\u67d0\u79cd\u75be\u75c5\u3002\u68c0\u6d4b\u8fd9\u79cd\u75be\u75c5\u7684\u6d4b\u8bd5\u5bf9\u4e8e\u9633\u6027\u75c5\u4f8b\u7684\u51c6\u786e\u7387\u662f 95%\uff0c\u5bf9\u4e8e\u9634\u6027\u75c5\u4f8b\u7684\u51c6\u786e\u7387\u662f 90%\u3002\u5982\u679c\u968f\u673a\u9009\u62e9\u7684\u4e00\u4e2a\u4eba\u68c0\u6d4b\u5448\u9633\u6027\uff0c\u4ed6\u4eec\u5b9e\u9645\u4e0a\u60a3\u6709\u8fd9\u79cd\u75be\u75c5\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__FFF8E1\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#FFF8E1\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u7ec3\u4e60\u9648\u8ff0\u7ed9\u4e86\u6211\u4eec\u4ee5\u4e0b\u6982\u7387\uff1a<\/p>\n<p class=\"has-text-align-center\"> A <sub>1<\/sub> : \u8be5\u4eba\u60a3\u6709\u75be\u75c5 \u2192 P(A <sub>1<\/sub> )=0.01<br \/> A <sub>2<\/sub> : \u8be5\u4eba\u6ca1\u6709\u60a3\u75c5 \u2192 P(A <sub>2<\/sub> )=0.99<\/p>\n<p class=\"has-text-align-center\"> B\uff1a\u68c0\u6d4b\u7ed3\u679c\u5448\u9633\u6027<br \/>B|A <sub>1<\/sub> \uff1a\u5f53\u8be5\u4eba\u60a3\u6709\u75be\u75c5\u65f6\u6d4b\u8bd5\u5448\u9633\u6027 \u2192 P(B|A <sub>1<\/sub> )=0.95<br \/> B|A <sub>2<\/sub> \uff1a\u5f53\u8be5\u4eba\u6ca1\u6709\u60a3\u75c5\u65f6\uff0c\u6d4b\u8bd5\u7ed3\u679c\u4e3a\u9633\u6027 \u2192 P(B|A <sub>2<\/sub> )=1-0.90=0.10<\/p>\n<p class=\"has-text-align-left\">\u7136\u540e\uff0c\u4e3a\u4e86\u8ba1\u7b97\u968f\u673a\u9009\u62e9\u7684\u4eba\u5728\u68c0\u6d4b\u5448\u9633\u6027\u65f6\u5b9e\u9645\u60a3\u6709\u8be5\u75be\u75c5\u7684\u6982\u7387\uff0c\u5fc5\u987b\u5e94\u7528\u8d1d\u53f6\u65af\u89c4\u5219\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c15e369635dcf17952b5d832a818d535_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A_i|B)=\\cfrac{P(B|A_i)\\cdot P(A_i)}{\\displaystyle \\sum_{k=1}^n P(B|A_k)\\cdot P(A_k)}\" title=\"Rendered by QuickLaTeX.com\" height=\"77\" width=\"251\" style=\"vertical-align: -49px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d76df126cb6076aeba65aa7d1c12e344_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A_1|B)=\\cfrac{P(B|A_1)\\cdot P(A_1)}{P(B|A_1)\\cdot P(A_1)+P(B|A_2)\\cdot P(A_2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"374\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6240\u4ee5\u6211\u4eec\u5c06\u8fd9\u4e9b\u503c\u4ee3\u5165\u516c\u5f0f\u5e76\u8fdb\u884c\u6982\u7387\u8ba1\u7b97\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-135e9ab7de6b44e7392fae0f5e70a125_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(A_1|B)&amp;=\\cfrac{P(B|A_1)\\cdot P(A_1)}{P(B|A_1)\\cdot P(A_1)+P(B|A_2)\\cdot P(A_2)}\\\\[2ex]&amp;=\\cfrac{0,95\\cdot 0,01}{0,95\\cdot 0,01+0,10\\cdot 0,99}\\\\[2ex]&amp;=0,0876\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"151\" width=\"374\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7b80\u800c\u8a00\u4e4b\uff0c\u968f\u673a\u9009\u62e9\u7684\u4e00\u4e2a\u4eba\u68c0\u6d4b\u5448\u9633\u6027\u4e14\u5b9e\u9645\u60a3\u6709\u8be5\u75be\u75c5\u7684\u6982\u7387\u4e3a 8.76%\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e602<\/h3>\n<p>\u636e\u4f30\u8ba1\uff0c\u4e00\u53ea\u80a1\u7968\u4e00\u5929\u5185\u4e0a\u6da8\u7684\u6982\u7387\u4e3a40%\uff0c\u4fdd\u6301\u7a33\u5b9a\u7684\u6982\u7387\u4e3a10%\uff0c\u4e0b\u8dcc\u7684\u6982\u7387\u4e3a50%\u3002\u6b64\u5916\uff0c\u6211\u4eec\u77e5\u9053\uff0c\u5f53\u5e02\u573a\u4e0a\u6da8\u65f6\uff0c\u91d1\u878d\u5206\u6790\u5e08\u9884\u6d4b\u6b63\u786e\u7684\u6982\u7387\u4e3a 90%\uff0c\u5f53\u5e02\u573a\u4fdd\u6301\u7a33\u5b9a\u65f6\uff0c\u9884\u6d4b\u6b63\u786e\u7684\u6982\u7387\u4e3a 75%\uff0c\u800c\u5f53\u5e02\u573a\u4e0b\u8dcc\u65f6\uff0c\u6b63\u786e\u9884\u6d4b\u7684\u6982\u7387\u4e3a 75%\u3002 85%.%\u3002\u5982\u679c\u5206\u6790\u5e08\u9884\u6d4b\u5e02\u573a\u5c06\u4e0b\u8dcc\uff0c\u90a3\u4e48\u5b9e\u9645\u4e0b\u8dcc\u7684\u53ef\u80fd\u6027\u6709\u591a\u5927\uff1f <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__FFF8E1\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#FFF8E1\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"><strong>\u67e5\u770b\u89e3\u51b3\u65b9\u6848<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\">\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u7ec3\u4e60\u8bed\u53e5\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u4ee5\u4e0b\u6982\u7387\uff1a<\/p>\n<p class=\"has-text-align-center\"> A <sub>1<\/sub> : \u4e00\u65e5\u884c\u60c5\u4e0a\u6da8 \u2192 P(A <sub>1<\/sub> )=0.40<br \/> A <sub>2<\/sub> : \u5e02\u573a\u5728\u4e00\u5929\u5185\u4fdd\u6301\u7a33\u5b9a \u2192 P(A <sub>2<\/sub> )=0.10<br \/> A <sub>3<\/sub> : \u4e00\u65e5\u884c\u60c5\u4e0a\u6da8 \u2192 P(A <sub>3<\/sub> )=0.50<\/p>\n<p class=\"has-text-align-center\"> B\uff1a\u5206\u6790\u5e08\u9884\u6d4b\u5e02\u573a\u5c06\u4f1a\u4e0b\u8dcc<br \/>B|A <sub>1<\/sub> \uff1a\u5206\u6790\u5e08\u6b63\u786e\u9884\u6d4b\u5e02\u573a\u5c06\u4f1a\u4e0a\u6da8 \u2192 P(B|A <sub>1<\/sub> )=0.90<br \/> B|A <sub>2<\/sub> \uff1a\u5206\u6790\u5e08\u6b63\u786e\u9884\u6d4b\u5e02\u573a\u4fdd\u6301\u7a33\u5b9a \u2192 P(B|A <sub>2<\/sub> )=0.75<br \/> B|A <sub>3<\/sub> \uff1a\u5206\u6790\u5e08\u6b63\u786e\u9884\u6d4b\u5e02\u573a\u5c06\u4e0b\u8dcc \u2192 P(B|A <sub>3<\/sub> )=0.85<\/p>\n<p class=\"has-text-align-left\">\u4e3a\u4e86\u786e\u5b9a\u5206\u6790\u5e08\u9884\u6d4b\u5e02\u573a\u5c06\u4e0b\u8dcc\u5e76\u4e14\u9884\u6d4b\u6b63\u786e\u7684\u6982\u7387\uff0c\u6211\u4eec\u9700\u8981\u4f7f\u7528\u8d1d\u53f6\u65af\u5b9a\u7406\u516c\u5f0f\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c15e369635dcf17952b5d832a818d535_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A_i|B)=\\cfrac{P(B|A_i)\\cdot P(A_i)}{\\displaystyle \\sum_{k=1}^n P(B|A_k)\\cdot P(A_k)}\" title=\"Rendered by QuickLaTeX.com\" height=\"77\" width=\"251\" style=\"vertical-align: -49px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7c2b74ac3ed5173c4a40837675d8282d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A_3|B)=\\cfrac{P(B|A_3)\\cdot P(A_3)}{P(B|A_1)\\cdot P(A_1)+P(B|A_2)\\cdot P(A_2)+ P(B|A_3)\\cdot P(A_3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"525\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6211\u4eec\u5c06\u6982\u7387\u503c\u4ee3\u5165\u8d1d\u53f6\u65af\u516c\u5f0f\u5e76\u8ba1\u7b97\u6982\u7387\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9f98a5a8a91299aa55aab02159dcebec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(A_3|B)&amp;=\\cfrac{P(B|A_3)\\cdot P(A_3)}{P(B|A_1)\\cdot P(A_1)+P(B|A_2)\\cdot P(A_2)+ P(B|A_3)\\cdot P(A_3)}\\\\[2ex]&amp;=\\cfrac{0,85\\cdot 0,50}{0,90\\cdot 0,40+0,75\\cdot 0,10+0,85\\cdot 0,50}\\\\[2ex]&amp;=0,4942\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"151\" width=\"525\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u5206\u6790\u5e08\u9884\u6d4b\u80a1\u5e02\u5c06\u4e0b\u8dcc\u7684\u6b63\u786e\u6982\u7387\u4e3a 49.42%\u3002<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f\u8d1d\u53f6\u65af\u5b9a\u7406\u4ee5\u53ca\u5b83\u5728\u6982\u7387\u548c\u7edf\u8ba1\u4e2d\u7684\u7528\u9014\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u4e86\u89e3\u8d1d\u53f6\u65af\u5b9a\u7406\u7684\u516c\u5f0f\u662f\u4ec0\u4e48\u3001\u8d1d\u53f6\u65af\u5b9a\u7406\u7684\u89e3\u51b3\u793a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-379","post","type-post","status-publish","format-standard","hentry","category-12"],"yoast_head":"<!-- This site is optimized with the 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