{"id":380,"date":"2023-08-01T11:32:01","date_gmt":"2023-08-01T11:32:01","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%85%a8%e6%a6%82%e7%8e%87%e5%ae%9a%e7%90%86\/"},"modified":"2023-08-01T11:32:01","modified_gmt":"2023-08-01T11:32:01","slug":"%e5%85%a8%e6%a6%82%e7%8e%87%e5%ae%9a%e7%90%86","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%85%a8%e6%a6%82%e7%8e%87%e5%ae%9a%e7%90%86\/","title":{"rendered":"\u603b\u6982\u7387\u5b9a\u7406"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4ec0\u4e48\u662f\u5168\u6982\u7387\u5b9a\u7406\u4ee5\u53ca\u5b83\u5728\u6982\u7387\u548c\u7edf\u8ba1\u4e2d\u7684\u7528\u9014\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u627e\u5230\u5168\u6982\u7387\u5b9a\u7406\u7684\u516c\u5f0f\u3001\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u4ee5\u53ca\u4f55\u65f6\u4f7f\u7528\u5168\u6982\u7387\u5b9a\u7406\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-teorema-de-la-probabilidad-total\"><\/span>\u4ec0\u4e48\u662f\u5168\u6982\u7387\u5b9a\u7406\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u6982\u7387\u8bba\u4e2d\uff0c<strong>\u5168\u6982\u7387\u5b9a\u7406<\/strong>\u662f\u4e00\u79cd\u5b9a\u5f8b\uff0c\u5b83\u4f7f\u5f97\u53ef\u4ee5\u6839\u636e\u6837\u672c\u7a7a\u95f4\u4e2d\u6240\u6709\u4e8b\u4ef6\u7684<a href=\"https:\/\/statorials.org\/cn\/\u6761\u4ef6\u6761\u4ef6\u6982\u7387\/\">\u6761\u4ef6\u6982\u7387<\/a>\u6765\u8ba1\u7b97\u4e0d\u5c5e\u4e8e\u6837\u672c\u7a7a\u95f4\u7684\u4e8b\u4ef6\u7684\u6982\u7387\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u603b\u6982\u7387\u5b9a\u7406\u7528\u4e8e\u6839\u636e\u6709\u5173\u7279\u5b9a\u4e8b\u4ef6\u7684\u90e8\u5206\u4fe1\u606f\u6765\u8ba1\u7b97\u8be5\u4e8b\u4ef6\u7684\u6982\u7387\u3002\u6709\u65f6\u6211\u4eec\u65e0\u6cd5\u901a\u8fc7\u76f4\u63a5\u5e94\u7528\u62c9\u666e\u62c9\u65af\u89c4\u5219\u6765\u786e\u5b9a\u4e8b\u4ef6\u7684\u6982\u7387\uff0c\u56e0\u4e3a\u6211\u4eec\u6ca1\u6709\u6240\u6709\u5fc5\u8981\u7684\u4fe1\u606f\u3002\u4f46\u662f\uff0c\u5982\u679c\u6211\u4eec\u77e5\u9053\u8be5\u4e8b\u4ef6\u76f8\u5bf9\u4e8e\u5176\u4ed6\u4e8b\u4ef6\u7684\u6570\u636e\uff0c\u5219\u603b\u6982\u7387\u5b9a\u7406\u901a\u5e38\u5f88\u6709\u7528\u3002<\/p>\n<p>\u7b80\u800c\u8a00\u4e4b\uff0c\u5f53\u6211\u4eec\u60f3\u8981\u8ba1\u7b97\u4e00\u4e2a\u4e8b\u4ef6\u7684\u6982\u7387\u4f46\u53ea\u5728\u67d0\u4e9b\u6761\u4ef6\u4e0b\u6709\u5173\u4e8e\u5b83\u7684\u4fe1\u606f\u65f6\uff0c\u5c31\u4f7f\u7528\u603b\u6982\u7387\u5b9a\u7406\u3002\u4f8b\u5982\uff0c\u8be5\u5b9a\u7406\u7684\u4e00\u4e9b\u5e94\u7528\u6d89\u53ca\u591a\u4e2a\u6848\u4f8b\u7684\u5b9e\u9a8c\u3001\u6392\u961f\u8bba\u548c\u751f\u5b58\u5206\u6790\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\/\u62c9\u666e\u62c9\u65af\u6cd5\u5219\u6216\u62c9\u666e\u62c9\u65af\u5b9a\u5f8b\/\">\u62c9\u666e\u62c9\u65af\u6cd5\u5219<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-teorema-de-la-probabilidad-total\"><\/span>\u5168\u6982\u7387\u5b9a\u7406\u7684\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u603b\u6982\u7387\u5b9a\u7406\u8868\u793a\uff0c\u7ed9\u5b9a\u4e00\u7ec4\u4e8b\u4ef6{A <sub>1<\/sub> , A <sub>2<\/sub> ,\u2026, A <sub>n<\/sub> }\uff0c\u5b83\u4eec\u5728\u6837\u672c\u7a7a\u95f4\u4e0a\u5f62\u6210\u4e00\u4e2a\u5206\u533a\uff0c\u4e8b\u4ef6 B \u7684\u6982\u7387\u7b49\u4e8e\u6bcf\u4e2a\u4e8b\u4ef6\u7684\u6982\u7387\u7684\u4e58\u79ef\u4e4b\u548c\u3002\u4e8b\u4ef6 P(A <sub>i<\/sub> ) \u7531\u6761\u4ef6\u6982\u7387 P(B|A <sub>i<\/sub> ) \u51b3\u5b9a\u3002<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u5168\u6982\u7387\u5b9a\u7406\u7684\u516c\u5f0f<\/strong>\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-probabilite-totale.png\" alt=\"\u5168\u6982\u7387\u5b9a\u7406\u516c\u5f0f\" class=\"wp-image-8595\" width=\"291\" height=\"320\" 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-3cf84b3bfcc955798a43fce91458ff42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"41\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u662f\u4e8b\u4ef6 B \u53d1\u751f\u7684\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\u3002<\/li>\n<\/ul>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u5728\u6982\u7387\u4e2d\uff0c\u6837\u672c\u7a7a\u95f4\u7684\u5206\u533a\u88ab\u5b9a\u4e49\u4e3a\u4e00\u7ec4\u76f8\u4e92\u4e0d\u517c\u5bb9\u7684\u4e8b\u4ef6\uff0c\u5176\u5e76\u96c6\u5f62\u6210\u6837\u672c\u7a7a\u95f4\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\/\u6837\u672c\u7a7a\u95f41\/\">\u6837\u672c\u7a7a\u95f4<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-resuelto-del-teorema-de-la-probabilidad-total\"><\/span>\u5168\u6982\u7387\u5b9a\u7406\u7684\u5177\u4f53\u4f8b\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u4e86\u89e3\u4e86\u5168\u6982\u7387\u5b9a\u7406\u7684\u5b9a\u4e49\u53ca\u5176\u516c\u5f0f\u4e4b\u540e\uff0c\u6211\u4eec\u5c06\u770b\u5230\u4e00\u4e2a\u5173\u4e8e\u5982\u4f55\u4f7f\u7528\u5168\u6982\u7387\u5b9a\u7406\u8ba1\u7b97\u6982\u7387\u7684\u5df2\u89e3\u51b3\u7ec3\u4e60\uff0c\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u5176\u542b\u4e49\u3002<\/p>\n<ul>\n<li>\u4e00\u5bb6\u7535\u5b50\u5546\u5e97\u9500\u552e\u4e09\u79cd\u54c1\u724c\u7684\u7535\u89c6\uff1aX\u3001Y\u3001Z\u3002\u636e\u4f30\u8ba1\uff0c\u54c1\u724c\u7535\u89c6\u5360\u9500\u552e\u989d\u7684 20%\uff0c\u6b21\u54c1\u54c1\u724c\u7535\u89c6\u5360\u9500\u552e\u989d\u7684 %\uff0cZ \u54c1\u724c\u7535\u89c6\u5360\u9500\u552e\u989d\u7684 4%\u3002\u7535\u89c6\u6709\u7f3a\u9677\u3002\u8d2d\u4e70\u6709\u7f3a\u9677\u7535\u89c6\u7684\u53ef\u80fd\u6027\u6709\u591a\u5927\uff1f<\/li>\n<\/ul>\n<p>\u95ee\u9898\u9648\u8ff0\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<sub>\u67d0\u4e2a<\/sub>\u54c1\u724c\u7684\u7535\u89c6<\/li>\n<li>\u4e8b\u4ef6 A <sub>2<\/sub> \uff1a\u987e\u5ba2\u8d2d\u4e70\u54c1\u724c Y \u7684\u7535\u89c6 \u2192 P(A <sub>2<\/sub> )=0.50<\/li>\n<li>\u4e8b\u4ef6 A <sub>3<\/sub> \uff1a\u987e\u5ba2\u8d2d\u4e70\u7535\u89c6\u54c1\u724c Z \u2192 P(A <sub>3<\/sub> )=0.30<\/li>\n<\/ul>\n<p>\u6b64\u5916\uff0c\u7ec3\u4e60\u8bed\u53e5\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\u4e2a\u54c1\u724c\u7684\u7535\u89c6 Y\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>\u56e0\u6b64\uff0c\u95ee\u9898\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=\"\" class=\"wp-image-8525\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u56e0\u6b64\uff0c\u8981\u8ba1\u7b97\u8d2d\u4e70\u6709\u7f3a\u9677\u7535\u89c6\u7684\u6982\u7387\uff0c\u6211\u4eec\u9700\u8981\u4f7f\u7528\u603b\u6982\u7387\u89c4\u5219\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-4bd2e4c30e05d7abab89dabb7b85cd6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P(B)=\\sum_{i=1}^n P(B|A_i)\\cdot P(A_i)\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"218\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<p>\u5728\u6211\u4eec\u7684\u4f8b\u5b50\u4e2d\uff0c\u6837\u672c\u7a7a\u95f4\u7531\u4e09\u4e2a\u4e8b\u4ef6\uff08A <sub>1<\/sub> \u3001A <sub>2<\/sub>\u548c A <sub>3<\/sub> \uff09\u7ec4\u6210\uff0c\u56e0\u6b64\u603b\u6982\u7387\u5b9a\u7406\u7684\u516c\u5f0f\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-0fe9d6f5c6241bf124144269ba498188_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P(B)=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=\"19\" width=\"496\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u7528\u524d\u9762\u7684\u8868\u8fbe\u5f0f\u7684\u6982\u7387\u6765\u8ba1\u7b97\u8d2d\u4e70\u6709\u7f3a\u9677\u7535\u89c6\u7684\u6982\u7387\u5c31\u8db3\u591f\u4e86\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-78411084ca76e5e0de6a2b1794e61b28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(B)&amp;=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;=0,05\\cdot 0,20+0,03\\cdot 0,50+0,04\\cdot 0,30\\\\[2ex]&amp;=0,037\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"496\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u603b\u4e4b\uff0c\u6211\u4eec\u8d2d\u4e70\u7684\u7535\u89c6\u6709\u7f3a\u9677\u7684\u6982\u7387\u4e3a 3.7%\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"teorema-de-la-probabilidad-total-y-teorema-de-bayes\"><\/span>\u5168\u6982\u7387\u5b9a\u7406\u548c\u8d1d\u53f6\u65af\u5b9a\u7406<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u603b\u6982\u7387\u5b9a\u7406\u548c\u8d1d\u53f6\u65af\u5b9a\u7406\u662f\u6982\u7387\u8bba\u4e2d\u7684\u4e24\u4e2a\u91cd\u8981\u5b9a\u7406\uff0c\u7279\u522b\u662f\u56e0\u4e3a\u5b83\u4eec\u5141\u8bb8\u6211\u4eec\u6839\u636e\u6761\u4ef6\u6982\u7387\u503c\u8ba1\u7b97\u6982\u7387\u3002<\/p>\n<p>\u8d1d\u53f6\u65af\u5b9a\u7406\u662f\u6982\u7387\u8bba\u5b9a\u5f8b\uff0c\u7528\u4e8e\u5728\u5df2\u77e5\u6709\u5173\u4e8b\u4ef6\u7684\u5148\u9a8c\u4fe1\u606f\u65f6\u8ba1\u7b97\u8be5\u4e8b\u4ef6\u7684\u6982\u7387\u3002<\/p>\n<p>\u5177\u4f53\u6765\u8bf4\uff0c<strong>\u5168\u6982\u7387\u5b9a\u7406\u548c\u8d1d\u53f6\u65af\u5b9a\u7406<\/strong>\u662f\u76f8\u5173\u7684\uff0c\u5b9e\u9645\u4e0a\u8d1d\u53f6\u65af\u5b9a\u7406\u516c\u5f0f\u7684\u5206\u6bcd\u5c31\u7b49\u4ef7\u4e8e\u5168\u6982\u7387\u5b9a\u7406\u516c\u5f0f\u3002<\/p>\n<p>\u5355\u51fb\u4ee5\u4e0b\u94fe\u63a5\u67e5\u770b\u8d1d\u53f6\u65af\u5b9a\u7406\u662f\u4ec0\u4e48\u53ca\u5176\u5e94\u7528\u793a\u4f8b\uff1a 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