{"id":39,"date":"2023-08-06T08:15:33","date_gmt":"2023-08-06T08:15:33","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%9d%a1%e4%bb%b6%e6%9d%a1%e4%bb%b6%e6%a6%82%e7%8e%87\/"},"modified":"2023-08-06T08:15:33","modified_gmt":"2023-08-06T08:15:33","slug":"%e6%9d%a1%e4%bb%b6%e6%9d%a1%e4%bb%b6%e6%a6%82%e7%8e%87","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%9d%a1%e4%bb%b6%e6%9d%a1%e4%bb%b6%e6%a6%82%e7%8e%87\/","title":{"rendered":"\u6761\u4ef6\u6982\u7387\uff08\u6216\u6761\u4ef6\u6982\u7387\uff09"},"content":{"rendered":"<p>\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u6761\u4ef6\u6982\u7387\uff08\u6216\u6761\u4ef6\u6982\u7387\uff09\u3002\u6211\u4eec\u901a\u8fc7\u793a\u4f8b\u89e3\u91ca\u5982\u4f55\u8ba1\u7b97\u6761\u4ef6\u6982\u7387\u4ee5\u53ca\u6b64\u7c7b\u6982\u7387\u7684\u5c5e\u6027\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u901a\u8fc7\u9010\u6b65\u89e3\u51b3\u7684\u6761\u4ef6\u6982\u7387\u7ec3\u4e60\u8fdb\u884c\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-probabilidad-condicional\"><\/span>\u4ec0\u4e48\u662f\u6761\u4ef6\u6982\u7387\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u6761\u4ef6\u6982\u7387<\/strong>\uff0c\u4e5f\u79f0\u4e3a<strong>\u6761\u4ef6\u6982\u7387<\/strong>\uff0c\u662f\u4e00\u79cd\u7edf\u8ba1\u5ea6\u91cf\uff0c\u8868\u793a\u5982\u679c\u53e6\u4e00\u4e2a\u4e8b\u4ef6 B \u53d1\u751f\uff0c\u5219\u4e8b\u4ef6 A \u53d1\u751f\u7684\u6982\u7387\u3002\u5373\uff0c\u6761\u4ef6\u6982\u7387P(A|B)\u662f\u6307\u4e8b\u4ef6B\u5df2\u7ecf\u53d1\u751f\u4e4b\u540e\u4e8b\u4ef6A\u53d1\u751f\u7684\u6982\u7387\u3002<\/p>\n<p>\u6761\u4ef6\u6982\u7387\u5728\u4e24\u4e2a\u4e8b\u4ef6\u4e4b\u95f4\u7528\u7ad6\u7ebf\u4e66\u5199\uff1aP(A|B)\uff0c\u5185\u5bb9\u4e3a\uff1a\u201c\u7ed9\u5b9a\u4e8b\u4ef6 B \u65f6\u4e8b\u4ef6 A \u7684\u6761\u4ef6\u6982\u7387\u201d\u3002<\/p>\n<p>\u8bf7\u6ce8\u610f\uff0c\u6761\u4ef6\u6982\u7387\u503c\u662f 0 \u5230 1 \u4e4b\u95f4\u7684\u6570\u5b57\u3002\u6761\u4ef6\u6982\u7387\u8d8a\u9ad8\uff0c\u4e8b\u4ef6 B \u53d1\u751f\u65f6\u4e8b\u4ef6 A \u53d1\u751f\u7684\u53ef\u80fd\u6027\u8d8a\u5927\uff0c\u4f46\u6761\u4ef6\u6982\u7387\u8d8a\u4f4e\uff0c\u4e8b\u4ef6 A \u53d1\u751f\u7684\u53ef\u80fd\u6027\u8d8a\u5c0f\u5f53\u4e8b\u4ef6 B \u53d1\u751f\u65f6\uff0c\u4e5f\u4f1a\u53d1\u751f\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-probabilidad-condicional\"><\/span>\u6761\u4ef6\u6982\u7387\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u4e8b\u4ef6 A \u7ed9\u5b9a\u4e8b\u4ef6 B \u7684\u6761\u4ef6\u6982\u7387<\/strong>\u7b49\u4e8e\u4e8b\u4ef6 A \u548c\u4e8b\u4ef6 B \u76f8\u4ea4\u7684\u6982\u7387\u9664\u4ee5\u4e8b\u4ef6 B \u7684\u6982\u7387\u3002 <\/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\/probabilite-conditionnelle-ou-conditionnelle.png\" alt=\"\u6761\u4ef6\u6216\u6761\u4ef6\u6982\u7387\" class=\"wp-image-634\" style=\"width:242px;height:243px\" width=\"242\" height=\"243\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u6ce8\u610f\uff0c\u53ea\u6709\u5f53\u65e0\u6761\u4ef6\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\u975e\u96f6\uff0c\u5373P(B)\u22600\u65f6\uff0c\u624d\u53ef\u4ee5\u4f7f\u7528\u6761\u4ef6\u6982\u7387\uff08\u6216\u6761\u4ef6\u6982\u7387\uff09\u516c\u5f0f\u3002\u6216\u8005\u6362\u53e5\u8bdd\u8bf4\uff0c\u4e8b\u4ef6B\u662f\u5426\u6709\u53ef\u80fd\u53d1\u751f\u3002<\/p>\n<p>\u6761\u4ef6\u6982\u7387\u4e5f\u53ef\u4ee5\u4ece\u5176\u5012\u6570\u8ba1\u7b97\u51fa\u6765\uff0c\u5373\u5982\u679cP(B|A)\u5df2\u77e5\uff0c\u5219\u53ef\u4ee5\u786e\u5b9aP(A|B)\u3002\u4f46\u8981\u505a\u5230\u8fd9\u4e00\u70b9\uff0c\u4f60\u5fc5\u987b\u5e94\u7528\u8d1d\u53f6\u65af\u5b9a\u7406\uff0c\u4f60\u53ef\u4ee5\u5728\u8fd9\u91cc\u770b\u5230\u8fd9\u4e2a\u5b9a\u7406\u7684\u5185\u5bb9\uff1a <\/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\/\u7edf\u8ba1\u5b66\u4ee5\u7b80\u5355\u76f4\u63a5\u7684\u65b9\u5f0f\u89e3\u91ca\u6982\u5ff5\uff0c\u6211\u4eec\u4f7f\u5b66\u4e60\u7edf\u8ba1\u53d8\u5f97\u66f4\u5bb9\u6613\/\">\u4ec0\u4e48\u662f\u8d1d\u53f6\u65af\u5b9a\u7406\uff1f<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-probabilidad-condicional\"><\/span>\u6761\u4ef6\u6982\u7387\u7684\u4f8b\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u6761\u4ef6\u6982\u7387\u7684\u5b9a\u4e49\u548c\u516c\u5f0f\u662f\u4ec0\u4e48\uff0c\u6211\u4eec\u5c06\u9010\u6b65\u89e3\u51b3\u6b64\u7c7b\u6982\u7387\u7684\u793a\u4f8b\uff0c\u4ee5\u5145\u5206\u7406\u89e3\u5176\u542b\u4e49\u3002<\/p>\n<ul>\n<li>\u5728\u5bf9\u4e00\u4e2a 30 \u540d\u5b66\u751f\u7684\u73ed\u7ea7\u8fdb\u884c\u8003\u8bd5\u540e\uff0c\u6211\u4eec\u6536\u96c6\u4e86\u6570\u636e\u4ee5\u4e86\u89e3\u6709\u591a\u5c11\u5b66\u751f\u5b66\u4e60\u4e86\u4ee5\u53ca\u6709\u591a\u5c11\u4eba\u901a\u8fc7\u4e86\u8003\u8bd5\u3002\u7ed3\u679c\u5217\u4e8e\u4ee5\u4e0b\u5217\u8054\u8868\u4e2d\u3002\u6839\u636e\u6536\u96c6\u7684\u6570\u636e\uff0c\u8ba1\u7b97\u901a\u8fc7\u8003\u8bd5\u7684\u6761\u4ef6\u6982\u7387\uff08\u5982\u679c\u60a8\u5df2\u7ecf\u5b66\u4e60\u8fc7\uff09\u3002 <\/li>\n<\/ul>\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\/exercice-de-probabilite-conditionnelle-resolu-1.png\" alt=\"\u6761\u4ef6\u6982\u7387\u7ec3\u4e60\u5df2\u89e3\u51b3\" class=\"wp-image-636\" style=\"width:386px;height:198px\" width=\"386\" height=\"198\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u4e3a\u4e86\u83b7\u5f97\u6761\u4ef6\u6982\u7387\uff0c\u6211\u4eec\u5fc5\u987b\u5e94\u7528\u4e4b\u524d\u770b\u5230\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-33399a41feb2bb4bbefd2acd9bc4541a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{aprobado}|\\text{estudiado})=\\cfrac{P(\\text{aprobado}\\cap\\text{estudiado})}{P(\\text{estudiado})}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"398\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u9996\u5148\u9700\u8981\u6c42\u51fa\u4e00\u4e2a\u5b66\u751f\u5b66\u4e60\u518d\u5b66\u4e60\u5e76\u901a\u8fc7\u7684\u6982\u7387\u3002\u8981\u627e\u5230\u5b66\u751f\u5b66\u4e60\u7684\u6982\u7387\uff0c\u6211\u4eec\u53ea\u9700\u4f7f\u7528\u62c9\u666e\u62c9\u65af\u89c4\u5219\uff0c\u5373\u5c06\u5b66\u4e60\u7684\u5b66\u751f\u4eba\u6570\u9664\u4ee5\u89c2\u5bdf\u603b\u6570\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-68484f319a736ae4c3dbf556fe5476d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{estudiado})=\\cfrac{23}{30}=0,77\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"203\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5b66\u4e60\u5e76\u901a\u8fc7\u7684\u5b66\u751f\u4eba\u6570\u9664\u4ee5\u603b\u6570\uff0c\u4ece\u5217\u8054\u8868\u4e2d\u627e\u51fa\u5b66\u751f\u540c\u65f6\u5b66\u4e60\u548c\u901a\u8fc7\u7684\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-1099d332a45dd54996a7fa373aeb8bba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{aprobado}\\cap \\text{estudiado})=\\cfrac{19}{30}=0,63\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"295\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u5982\u679c\u5b66\u751f\u5df2\u7ecf\u5b66\u4e60\uff0c\u4ed6\u901a\u8fc7\u8003\u8bd5\u7684\u6982\u7387\u4e3a\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-b93263fb386c7978bd9b5cf886b47377_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(\\text{aprobado}|\\text{estudiado})&amp;=\\cfrac{P(\\text{aprobado}\\cap\\text{estudiado})}{P(\\text{estudiado})}\\\\ &amp;=\\cfrac{0,63}{0,77}\\\\[1.5ex] &amp;=0,82\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"132\" width=\"398\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"probabilidad-condicional-de-eventos-dependientes-e-independientes\"><\/span>\u76f8\u5173\u4e8b\u4ef6\u548c\u72ec\u7acb\u4e8b\u4ef6\u7684\u6761\u4ef6\u6982\u7387<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u4e86\u89e3\u6761\u4ef6\u6982\u7387\u4e0e\u76f8\u5173\u4e8b\u4ef6\u548c\u72ec\u7acb\u4e8b\u4ef6\uff08\u6216\u76f8\u5173\u4e8b\u4ef6\u548c\u72ec\u7acb\u4e8b\u4ef6\uff09\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u56e0\u4e3a\uff0c\u867d\u7136\u5b83\u4eec\u662f\u4e0d\u540c\u7684\u6982\u5ff5\uff0c\u4f46\u8fd9\u4e24\u79cd\u7c7b\u578b\u7684\u4e8b\u4ef6\u90fd\u4e0e\u6761\u4ef6\u6982\u7387\u76f8\u5173\u3002<\/p>\n<p>\u5f53\u4e24\u4e2a\u4e8b\u4ef6\uff08\u6216\u4e8b\u4ef6\uff09\u53d1\u751f\u7684\u6982\u7387\u4e0d\u76f8\u4e92\u4f9d\u8d56\u65f6\uff0c\u5b83\u4eec\u5c31\u662f\u72ec\u7acb\u7684\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4e24\u4e2a\u4e8b\u4ef6\u4e4b\u95f4\u7684\u4ea4\u96c6\u76f8\u5f53\u4e8e\u6bcf\u4e2a\u4e8b\u4ef6\u5404\u81ea\u7684\u6982\u7387\u7684\u4e58\u79ef\u3002\u56e0\u6b64\uff0c\u6761\u4ef6\u6982\u7387\u516c\u5f0f\u88ab\u7b80\u5316\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-49686492cfff4e71fa15d8911383ca53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A|B)=\\cfrac{P(A\\cap B)}{P(B)}=\\cfrac{P(A)\\cdot P(B)}{P(B)}=P(A)\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"345\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u7b80\u800c\u8a00\u4e4b\uff0c<strong>\u5982\u679c\u4e8b\u4ef6 A \u548c B \u662f\u72ec\u7acb\u7684\uff0c\u5219\u4e8b\u4ef6 A \u7ed9\u5b9a\u4e8b\u4ef6 B \u7684\u6761\u4ef6\u6982\u7387\u6070\u597d\u7b49\u4e8e\u4e8b\u4ef6 A \u53d1\u751f\u7684\u6982\u7387\u3002<\/strong><\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u5f53\u4e24\u4e2a\u4e8b\u4ef6\u76f8\u5173\u65f6\uff0c\u610f\u5473\u7740\u4e00\u4e2a\u4e8b\u4ef6\u7684\u6982\u7387\u53d6\u51b3\u4e8e\u53e6\u4e00\u4e2a\u4e8b\u4ef6\u7684\u6982\u7387\u3002\u56e0\u6b64\uff0c<strong>\u5f53\u4e24\u4e2a\u4e8b\u4ef6 A \u548c B \u76f8\u5173\u65f6\uff0c\u4e8b\u4ef6 A \u7ed9\u5b9a\u4e8b\u4ef6 B \u7684\u6761\u4ef6\u6982\u7387\u4e0e\u4e8b\u4ef6 A \u53d1\u751f\u7684\u6982\u7387\u4e0d\u540c\u3002<\/strong> <\/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-467a5f0e02c42a9faf9cb06dcc039573_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A|B)\\neq P(A)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-probabilidad-condicional\"><\/span>\u89e3\u51b3\u4e86\u6761\u4ef6\u6982\u7387\u7ec3\u4e60<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e601<\/h3>\n<p>\u6211\u4eec\u77e5\u9053\uff0c\u5728\u88c5\u6ee1\u7403\u7684\u888b\u5b50\u91cc\uff0c\u4e00\u534a\u662f\u6a59\u8272\u7684\uff0c\u53e6\u4e00\u534a\u662f\u7eff\u8272\u7684\u3002\u6b64\u5916\uff0c\u4e09\u5206\u4e4b\u4e00\u7684\u7403\u662f\u6a59\u8272\u7684\uff0c\u540c\u65f6\u6807\u6709\u6807\u5fd7\u3002\u5f53\u4f60\u753b\u4e00\u4e2a\u6a59\u8272\u7684\u7403\u65f6\uff0c\u5b83\u6536\u5230\u4fe1\u53f7\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\">\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u7ec3\u4e60\uff0c\u6211\u4eec\u5fc5\u987b\u5e94\u7528\u6761\u4ef6\u6982\u7387\u516c\u5f0f\uff0c\u5373\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-dd455568aecf096a117cd3469ef623b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{se\\~nal}|\\text{naranja})=\\cfrac{P(\\text{se\\~nal}\\cap\\text{naranja})}{P(\\text{naranja})}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"300\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u95ee\u9898\u9648\u8ff0\u544a\u8bc9\u6211\u4eec\uff0c\u888b\u5b50\u7684\u4e00\u534a\u662f\u6a59\u5b50\u3002\u56e0\u6b64\uff0c\u7406\u8bba\u4e0a\u6361\u5230\u6a59\u8272\u7403\u7684\u6982\u7387\u662f50%\u3002<\/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-c6bfa6b17a6eddb7b741f1878436bf91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{naranja})=\\cfrac{1}{2}=0,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"169\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u53e6\u4e00\u65b9\u9762\uff0c\u6211\u4eec\u77e5\u9053\u603b\u6570\u7684\u4e09\u5206\u4e4b\u4e00\u662f\u6a59\u8272\u7403\u5e76\u4e14\u6709\u4fe1\u53f7\uff0c\u56e0\u6b64\u83b7\u5f97\u5e26\u6709\u4fe1\u53f7\u7684\u6a59\u8272\u7403\u7684\u6982\u7387\u4e3a\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-9f693380c8a1144f899e8c90bf36735b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{se\\~nal}\\cap \\text{naranja})=\\cfrac{1}{3}=0,33\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"237\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u6700\u540e\uff0c\u6211\u4eec\u5c06\u8ba1\u7b97\u51fa\u7684\u6982\u7387\u4ee3\u5165\u6761\u4ef6\u6982\u7387\u516c\u5f0f\u6c42\u5f97\u5176\u503c\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-66a7a5e06952a839c7d76ee5555b3400_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(\\text{se\\~nal}|\\text{naranja})&amp;=\\cfrac{P(\\text{se\\~nal}\\cap\\text{naranja})}{P(\\text{naranja})}\\\\ &amp;=\\cfrac{0,33}{0,5}\\\\[1.5ex] &amp;=0,66\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"132\" width=\"300\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u603b\u4e4b\uff0c\u5982\u679c\u4fe1\u53f7\u662f\u6a59\u8272\uff0c\u5219\u62bd\u5230\u7403\u7684\u6982\u7387\u4e3a 66%\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>\u5982\u679c\u6211\u4eec\u5728\u4e00\u4e2a\u76d2\u5b50\u91cc\u6709\u516d\u652f\u84dd\u7b14\u548c\u4e09\u652f\u9ed1\u7b14\uff0c\u8ba1\u7b97\u753b\u51fa\u4e00\u652f\u84dd\u7b14\u7684\u6982\u7387\u548c\u8fde\u7eed\u753b\u51fa\u4e24\u652f\u84dd\u7b14\u7684\u6982\u7387\u3002 <\/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\">\u8981\u786e\u5b9a\u62ff\u8d77\u84dd\u7b14\u4e00\u6b21\u7684\u6982\u7387\uff0c\u53ea\u9700\u4f7f\u7528\u62c9\u666e\u62c9\u65af\u5b9a\u5f8b\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-7a3eb3a04c9488adbbae6ef72252942c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{azul})=\\cfrac{6}{6+3}=0,67\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"183\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u8be5\u95ee\u9898\u8fd8\u8981\u6c42\u6211\u4eec\u77e5\u9053\u8fde\u7eed\u62ff\u8d77\u4e24\u652f\u84dd\u7b14\u7684\u6982\u7387\uff0c\u5373\u5982\u679c\u6211\u4eec\u4e4b\u524d\u5df2\u7ecf\u62ff\u8d77\u4e86\u4e00\u652f\u84dd\u7b14\uff0c\u5219\u62ff\u8d77\u4e00\u652f\u84dd\u7b14\u7684\u6761\u4ef6\u6982\u7387\u3002<\/p>\n<p class=\"has-text-align-left\">\u5982\u679c\u6211\u4eec\u753b\u4e00\u652f\u84dd\u8272\u7b14\uff0c\u6211\u4eec\u7684\u60c5\u51b5\u5c31\u4e0d\u592a\u6709\u5229\uff0c\u4f46\u603b\u6570\u4e5f\u5c11\u4e86\u4e00\u652f\u3002\u56e0\u6b64\uff0c\u6761\u4ef6\u6982\u7387\u4e3a\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-9f38e858e7344dbfa6ba55957828eb93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{azul}|\\text{azul})=\\cfrac{5}{8}=0,63\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"188\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e603<\/h3>\n<p>\u5982\u679c\u629b\u786c\u5e01\u51fa\u73b0\u6b63\u9762\uff0c\u5219\u9ab0\u5b50\u63b7\u5230\u6570\u5b57 4 \u7684\u6761\u4ef6\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\">\u8981\u89e3\u51b3\u6b64\u7ec3\u4e60\uff0c\u60a8\u5fc5\u987b\u8003\u8651\u6761\u4ef6\u6982\u7387\u7406\u8bba\uff0c\u56e0\u4e3a<em>\u201c\u63b7\u9ab0\u5b50\u5f97\u5230\u6570\u5b57 4\u201d<\/em>\u548c<em>\u201c\u629b\u786c\u5e01\u5f97\u5230\u6b63\u9762\u201d<\/em>\u4e8b\u4ef6\u662f\u72ec\u7acb\u7684\u3002\u56e0\u6b64\u4e0d\u5fc5\u4f7f\u7528\u6761\u4ef6\u6982\u7387\u516c\u5f0f\uff0c\u4f46\u6ee1\u8db3\u4ee5\u4e0b\u7b49\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-cba2c41d62c049264f84f186fd40f50f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{n\\'umero 4}|\\text{cara})=P(\\text{n\\'umero 4})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"261\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u8981\u627e\u5230\u6761\u4ef6\u6982\u7387\uff0c\u53ea\u9700\u4f7f\u7528\u62c9\u666e\u62c9\u65af\u89c4\u5219\u5373\u53ef\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-535fc22b3b3559d26411725a7ad749ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{n\\'umero 4}|\\text{cara})=P(\\text{n\\'umero 4})=\\cfrac{1}{6}=0,167\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"364\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u7ec3\u4e604<\/h3>\n<p>\u7814\u7a76\u4e86\u4e00\u4e2a\u56fd\u5bb6 25 \u5bb6\u516c\u53f8\u7684\u8d22\u653f\u5e74\u5ea6\u4ee5\u53ca\u5b83\u4eec\u7684\u80a1\u4ef7\u5982\u4f55\u6839\u636e\u5f53\u5e74\u7684\u7ecf\u6d4e\u7ed3\u679c\u53d8\u5316\u3002\u60a8\u53ef\u4ee5\u5728\u4ee5\u4e0b\u5217\u8054\u8868\u4e2d\u770b\u5230\u6536\u96c6\u7684\u6570\u636e\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\/exercice-de-probabilite-conditionnelle-resolu.png\" alt=\"\u6761\u4ef6\u6982\u7387\u7ec3\u4e60\u5df2\u89e3\u51b3\" class=\"wp-image-667\" style=\"width:344px;height:151px\" width=\"344\" height=\"151\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u5982\u679c\u4e00\u5bb6\u516c\u53f8\u5728\u8fc7\u53bb\u4e00\u5e74\u76c8\u5229\uff0c\u5176\u80a1\u4ef7\u4e0a\u6da8\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\">\u8be5\u7ec3\u4e60\u8be2\u95ee\u6211\u4eec\u5728\u516c\u53f8\u53d6\u5f97\u79ef\u6781\u7684\u7ecf\u6d4e\u6210\u679c\u7684\u60c5\u51b5\u4e0b\u80a1\u7968\u4e0a\u6da8\u7684\u6761\u4ef6\u6982\u7387\u3002\u56e0\u6b64\uff0c\u8981\u8ba1\u7b97\u8fd9\u4e2a\u6982\u7387\uff0c\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u6761\u4ef6\u6982\u7387\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-59ea2293eda9f4b28dc07bebd176cea4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{precio sube}|\\text{beneficio})=\\cfrac{P(\\text{precio sube}\\cap\\text{beneficio})}{P(\\text{beneficio})}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"416\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u56e0\u6b64\uff0c\u6211\u4eec\u9996\u5148\u8ba1\u7b97\u4e00\u5bb6\u516c\u53f8\u76c8\u5229\u7684\u6982\u7387\uff0c\u5176\u6b21\u8ba1\u7b97\u4e00\u5bb6\u516c\u53f8\u5728\u63d0\u9ad8\u6bcf\u80a1\u4ef7\u683c\u7684\u540c\u65f6\u83b7\u5f97\u7ecf\u6d4e\u5229\u6da6\u7684\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-fe323f1e5e9f9e0e8fc44e886a63b476_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{beneficio})=\\cfrac{14}{25}=0,56\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"197\" style=\"vertical-align: -12px;\"><\/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-32514b2dc97d679bd0946fb9ad6dc82a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{precio sube}\\cap\\text{beneficio})=\\cfrac{10}{25}=0,4 \" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"295\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u7136\u540e\u6211\u4eec\u5c06\u627e\u5230\u7684\u503c\u4ee3\u5165\u516c\u5f0f\u5e76\u8ba1\u7b97\u6761\u4ef6\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-9fdc17ed2f93c9122e9678f52ed88804_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(\\text{precio sube}|\\text{beneficio})&amp; =\\cfrac{P(\\text{precio sube}\\cap\\text{beneficio})}{P(\\text{beneficio})}\\\\ &amp;= \\cfrac{0,4}{0,56}\\\\[1.5ex]&amp; =0,71 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"132\" width=\"416\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-probabilidad-condicional\"><\/span>\u6761\u4ef6\u6982\u7387\u7684\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6761\u4ef6\u6982\u7387\u6216\u6761\u4ef6\u6982\u7387\u7684\u6027\u8d28\u5982\u4e0b\uff1a<\/p>\n<ul>\n<li>\u7ed9\u5b9a\u4e8b\u4ef6 B \u7684\u4e8b\u4ef6 A \u7684\u6761\u4ef6\u6982\u7387\u52a0\u4e0a\u7ed9\u5b9a\u4e8b\u4ef6 B \u7684\u4e92\u8865\u4e8b\u4ef6 A \u7684\u6761\u4ef6\u6982\u7387\u4e4b\u548c\u7b49\u4e8e 1\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-da7b3f0bad9cd194066ee9bfb12a0d96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P\\bigl(A|B\\bigr)+P\\bigl(\\overline{A}|B\\bigr)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"179\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<ul>\n<li>\u5982\u679c\u4e8b\u4ef6 A \u662f\u4e8b\u4ef6 B \u7684\u5b50\u96c6\uff0c\u5219\u5f53 B \u4e3a\u771f\u65f6\uff0cA \u5c06\u59cb\u7ec8\u53d1\u751f\u3002\u56e0\u6b64\uff0c\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\uff0c\u4e8b\u4ef6 A \u7ed9\u5b9a\u4e8b\u4ef6 B \u7684\u6761\u4ef6\u6982\u7387\u4e3a 1\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7c320188a6c5f661fd564a30d5f50516_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B\\subseteq A \\ \\longrightarrow \\ P(A|B)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li>\u7ed9\u5b9a\u4e24\u4e2a\u4e0d\u540c\u7684\u4e8b\u4ef6\uff0c\u4ee5\u4e0b\u5173\u4e8e\u6761\u4ef6\u6982\u7387\u7684\u7b49\u5f0f\u59cb\u7ec8\u6210\u7acb\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-71739d3a3422089d240ad2ee6cd846bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\\bigl(A\\bigr)=P\\bigl(A|B\\bigr)\\cdot P\\bigl(B\\bigr)+P\\bigl(A|\\overline{B}\\bigl)\\cdot P\\bigl(\\overline{B}\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"318\" style=\"vertical-align: 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