{"id":633,"date":"2025-12-13T13:35:29","date_gmt":"2025-12-13T05:35:29","guid":{"rendered":"https:\/\/book.yuekegu.com\/?p=633"},"modified":"2025-12-13T13:45:46","modified_gmt":"2025-12-13T05:45:46","slug":"%e6%9d%a1%e4%bb%b6%e6%a6%82%e7%8e%87%e3%80%81%e5%85%a8%e6%a6%82%e7%8e%87","status":"publish","type":"post","link":"https:\/\/book.yuekegu.com\/index.php\/2025\/12\/13\/%e6%9d%a1%e4%bb%b6%e6%a6%82%e7%8e%87%e3%80%81%e5%85%a8%e6%a6%82%e7%8e%87\/","title":{"rendered":"\u6761\u4ef6\u6982\u7387\u3001\u5168\u6982\u7387"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">\u6838\u5fc3\u5173\u8054\u6982\u5ff5<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6d89\u53ca\u4e8b\u4ef6\u7c7b\u578b\uff1a\u4e92\u65a5\u4e8b\u4ef6\u3001\u5bf9\u7acb\u4e8b\u4ef6\u3001\u72ec\u7acb\u4e8b\u4ef6<\/li>\n\n\n\n<li>\u5173\u952e\u7591\u95ee\uff1a\u4e92\u65a5\u4e0e\u76f8\u4e92\u72ec\u7acb\u7684\u5173\u7cfb\uff1f<\/li>\n\n\n\n<li>\u76f8\u5173\u516c\u5f0f\uff1a\u548c\u4e8b\u4ef6\u7684\u6982\u7387\u516c\u5f0f\u3001\u76f8\u4e92\u72ec\u7acb\u4e8b\u4ef6\u7684\u79ef\u4e8b\u4ef6\u6982\u7387\u516c\u5f0f<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u6761\u4ef6\u6982\u7387<\/h2>\n\n\n\n<p>\u4e00\u822c\u5730\uff0c\u8bbeA\u3001B\u4e3a\u4e24\u4e2a\u4e8b\u4ef6\uff0c\u4e14$P(A)&gt;0$\uff0c\u6211\u4eec\u79f0$\\frac{P(AB)}{P(A)}$\u4e3a\u4e8b\u4ef6A\u53d1\u751f\u7684\u6761\u4ef6\u4e0b\u4e8b\u4ef6B\u53d1\u751f\u7684\u6761\u4ef6\u6982\u7387\uff08conditional probability\uff09\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8bb0\u6cd5\uff1a$P(B|A)$<\/li>\n\n\n\n<li>\u8bfb\u6cd5\uff1a\u201cA\u53d1\u751f\u7684\u6761\u4ef6\u4e0bB\u53d1\u751f\u7684\u6982\u7387\u201d<\/li>\n\n\n\n<li>\u516c\u5f0f\uff1a$P(B | A)=\\frac{P(AB)}{P(A)}(P(A)>0)$<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u6982\u7387\u7684\u4e58\u6cd5\u516c\u5f0f<\/h2>\n\n\n\n<p>\u7531\u6761\u4ef6\u6982\u7387\u7684\u5b9a\u4e49\uff0c\u5bf9\u4efb\u610f\u4e24\u4e2a\u4e8b\u4ef6A\u4e0eB\uff0c\u82e5$P(A)&gt;0$\uff0c\u5219\uff1a<br>$P(AB)=P(A)P(B|A)$<br>\u4e0a\u5f0f\u79f0\u4e3a\u6982\u7387\u7684\u4e58\u6cd5\u516c\u5f0f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4f8b\u9898<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u7532\u888b\u4e2d\u67093\u4e2a\u767d\u7403\u548c2\u4e2a\u7ea2\u7403\uff0c\u4e59\u888b\u4e2d\u67092\u4e2a\u767d\u7403\u548c3\u4e2a\u7ea2\u7403\u3002\u5148\u968f\u673a\u53d6\u4e00\u53ea\u888b\uff0c\u518d\u4ece\u8be5\u888b\u4e2d\u968f\u673a\u53d6\u4e00\u4e2a\u7403\uff0c\u8be5\u7403\u4e3a\u7ea2\u7403\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f<\/li>\n\n\n\n<li>\uff08\u4f8b4\uff09\u8bbe\u7532\u888b\u4e2d\u67093\u4e2a\u767d\u7403\u548c4\u4e2a\u7ea2\u7403\uff0c\u4e59\u888b\u4e2d\u67091\u4e2a\u767d\u7403\u548c2\u4e2a\u7ea2\u7403\u3002\u73b0\u4ece\u7532\u888b\u4e2d\u4efb\u53d62\u4e2a\u7403\u653e\u5165\u4e59\u888b\uff0c\u518d\u4ece\u4e59\u888b\u4e2d\u4efb\u53d62\u4e2a\u7403\uff0c\u6c42\u4ece\u4e59\u888b\u4e2d\u53d6\u51fa\u7684\u662f2\u4e2a\u7ea2\u7403\u7684\u6982\u7387\u3002<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">\u5168\u6982\u7387\u516c\u5f0f<\/h2>\n\n\n\n<p>\u5168\u6982\u7387\u516c\u5f0f\u662f\u6307\u4e00\u4e2a\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\u662f\u5176\u5728\u4e0d\u540c\u6761\u4ef6\u4e0b\u53d1\u751f\u6982\u7387\u7684\u52a0\u6743\u5e73\u5747\uff0c\u662f\u7b80\u5355\u76f4\u89c2\u7684\u91cd\u8981\u516c\u5f0f\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u516c\u5f0f\u6761\u4ef6<\/h3>\n\n\n\n<p>\u82e5\u4e8b\u4ef6$A_{1},A_{2},\\cdots,A_{n}$\u4e24\u4e24\u4e92\u65a5\uff0c\u4e14\u5b83\u4eec\u7684\u548c$\\sum_{i=1}^{n}A_{i}=\\Omega$\uff0c\u540c\u65f6\u6ee1\u8db3$P(A_{i})&gt;0$\uff08$i=1,2,\\cdots,n$\uff09\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u516c\u5f0f\u5185\u5bb9<\/h3>\n\n\n\n<p>\u5bf9\u4e8e\u03a9\u4e2d\u7684\u4efb\u610f\u4e8b\u4ef6B\uff0c\u6709\uff1a<br>$P(B)=\\sum_{i=1}^{n}P(A_{i})P(B|A_{i})$<br>\u8be5\u516c\u5f0f\u79f0\u4e3a\u5168\u6982\u7387\u516c\u5f0f\uff08total probability formula\uff09\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6838\u5fc3\u5173\u8054\u6982\u5ff5 \u6761\u4ef6\u6982\u7387 \u4e00\u822c\u5730\uff0c\u8bbeA\u3001B\u4e3a\u4e24\u4e2a\u4e8b\u4ef6\uff0c\u4e14$P(A)&gt;0$\uff0c\u6211\u4eec\u79f0$\\frac{P(AB)}{P(A)}$\u4e3a\u4e8b\u4ef6A\u53d1\u751f\u7684\u6761\u4ef6\u4e0b\u4e8b\u4ef6B\u53d1\u751f\u7684\u6761\u4ef6\u6982\u7387\uff08conditional probability\uff09\u3002 \u6982\u7387\u7684\u4e58\u6cd5\u516c\u5f0f \u7531\u6761\u4ef6\u6982\u7387\u7684\u5b9a\u4e49\uff0c\u5bf9\u4efb\u610f\u4e24\u4e2a\u4e8b\u4ef6A\u4e0eB\uff0c\u82e5$P(A)&gt;0$\uff0c\u5219\uff1a$P(AB)=P(A)P(B|A)$\u4e0a\u5f0f\u79f0\u4e3a\u6982\u7387\u7684\u4e58\u6cd5\u516c\u5f0f\u3002 \u4f8b\u9898 \u5168\u6982\u7387\u516c\u5f0f \u5168\u6982\u7387\u516c\u5f0f\u662f\u6307\u4e00\u4e2a\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\u662f\u5176\u5728\u4e0d\u540c\u6761\u4ef6\u4e0b\u53d1\u751f\u6982\u7387\u7684\u52a0\u6743\u5e73\u5747\uff0c\u662f\u7b80\u5355\u76f4\u89c2\u7684\u91cd\u8981\u516c\u5f0f\u3002 \u516c\u5f0f\u6761\u4ef6 \u82e5\u4e8b\u4ef6$A_{1},A_{2},\\cdots,A_{n}$\u4e24\u4e24\u4e92\u65a5\uff0c\u4e14\u5b83\u4eec\u7684\u548c$\\sum_{i=1}^{n}A_{i}=\\Omega$\uff0c\u540c\u65f6\u6ee1\u8db3$P(A_{i})&gt;0$\uff08$i=1,2,\\cdots,n$\uff09\u3002 \u516c\u5f0f\u5185\u5bb9 \u5bf9\u4e8e\u03a9\u4e2d\u7684\u4efb\u610f\u4e8b\u4ef6B\uff0c\u6709\uff1a$P(B)=\\sum_{i=1}^{n}P(A_{i})P(B|A_{i})$\u8be5\u516c\u5f0f\u79f0\u4e3a\u5168\u6982\u7387\u516c\u5f0f\uff08total probability formula\uff09\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[45],"tags":[],"class_list":["post-633","post","type-post","status-publish","format-standard","hentry","category-45"],"_links":{"self":[{"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/posts\/633","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/comments?post=633"}],"version-history":[{"count":2,"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/posts\/633\/revisions"}],"predecessor-version":[{"id":635,"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/posts\/633\/revisions\/635"}],"wp:attachment":[{"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/media?parent=633"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/categories?post=633"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/book.yuekegu.com\/index.php\/wp-json\/wp\/v2\/tags?post=633"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}