{"id":37,"date":"2023-08-06T09:33:38","date_gmt":"2023-08-06T09:33:38","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e8%81%94%e5%90%88%e6%a6%82%e7%8e%87\/"},"modified":"2023-08-06T09:33:38","modified_gmt":"2023-08-06T09:33:38","slug":"%e8%81%94%e5%90%88%e6%a6%82%e7%8e%87","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e8%81%94%e5%90%88%e6%a6%82%e7%8e%87\/","title":{"rendered":"\u8054\u5408\u6982\u7387"},"content":{"rendered":"<p>\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u89e3\u91ca\u4ec0\u4e48\u662f\u8054\u5408\u6982\u7387\u4ee5\u53ca\u5b83\u662f\u5982\u4f55\u8ba1\u7b97\u7684\u3002\u60a8\u8fd8\u5c06\u627e\u5230\u8054\u5408\u6982\u7387\u7684\u793a\u4f8b\u4ee5\u53ca\u8054\u5408\u6982\u7387\u3001\u8fb9\u9645\u6982\u7387\u548c\u6761\u4ef6\u6982\u7387\u4e4b\u95f4\u7684\u533a\u522b\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-probabilidad-conjunta\"><\/span>\u4ec0\u4e48\u662f\u8054\u5408\u6982\u7387\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u8054\u5408\u6982\u7387<\/strong>\u662f\u4e00\u79cd\u7edf\u8ba1\u5ea6\u91cf\uff0c\u8868\u793a\u4e24\u4e2a\u4e8b\u4ef6\u540c\u65f6\u53d1\u751f\u7684\u6982\u7387\u3002<\/p>\n<p>\u6982\u7387\u7ec4\u5408\u662f0\u52301\u4e4b\u95f4\u7684\u6570\u5b57\u3002\u53ea\u8981\u6982\u7387\u7ec4\u5408\u8d8a\u5927\uff0c\u4e8b\u4ef6\u540c\u65f6\u53d1\u751f\u7684\u53ef\u80fd\u6027\u5c31\u8d8a\u5927\uff0c\u53cd\u4e4b\uff0c\u5982\u679c\u6982\u7387\u5927\u4e8e\u6982\u7387\u7ec4\u5408\uff0c\u5219\u4e8b\u4ef6\u540c\u65f6\u53d1\u751f\u7684\u53ef\u80fd\u6027\u5c31\u8d8a\u5c0f\u4e8b\u4ef6\u540c\u65f6\u53d1\u751f\u3002\u6b21\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-probabilidad-conjunta\"><\/span>\u8054\u5408\u6982\u7387\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u4e24\u4e2a\u4e8b\u4ef6 A \u548c B \u7684\u8054\u5408\u6982\u7387\u7b49\u4e8e\u4e8b\u4ef6 A \u7684\u6982\u7387\u4e58\u4ee5\u4e8b\u4ef6 B \u7684\u6982\u7387\u7684\u4e58\u79ef\u3002<\/strong><\/p>\n<p>\u56e0\u6b64\uff0c\u8ba1\u7b97\u4e24\u4e2a\u4e0d\u540c\u4e8b\u4ef6\u7684\u8054\u5408\u6982\u7387\u7684\u516c\u5f0f\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-593a1a131cab23d805d8324e21e6b4ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A\\cap B)=P(A)\\cdot P(B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u4e24\u4e2a\u4e0d\u540c\u4e8b\u4ef6\u7684\u8054\u5408\u6982\u7387\u76f8\u5f53\u4e8e\u8fd9\u4e9b\u4e8b\u4ef6\u7684\u4ea4\u96c6\u3002\u4f46\u662f\uff0c\u60a8\u5fc5\u987b\u8bb0\u4f4f\uff0c\u53ea\u6709\u5f53\u5b83\u4eec\u662f\u4e24\u4e2a<a href=\"https:\/\/statorials.org\/cn\/\u4e8b\u4ef6-\u72ec\u7acb\u4e8b\u4ef6\/\">\u72ec\u7acb\u4e8b\u4ef6<\/a>\u65f6\u624d\u53ef\u4ee5\u4f7f\u7528\u6b64\u516c\u5f0f\uff0c\u5426\u5219\u60a8\u5fc5\u987b\u4f7f\u7528<a href=\"https:\/\/statorials.org\/cn\/\u6761\u4ef6\u6761\u4ef6\u6982\u7387\/\">\u6761\u4ef6\u6982\u7387\u516c\u5f0f<\/a>\u3002<\/p>\n<p>\u6b64\u5916\uff0c\u4e24\u4e2a\u4e8b\u4ef6\u7684\u8054\u5408\u6982\u7387\u603b\u662f\u5c0f\u4e8e\u6bcf\u4e2a\u4e8b\u4ef6\u5355\u72ec\u53d1\u751f\u7684\u6982\u7387\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-probabilidad-conjunta\"><\/span>\u8054\u5408\u6982\u7387\u7684\u4f8b\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8003\u8651\u5230\u8054\u5408\u6982\u7387\u7684\u5b9a\u4e49\uff0c\u6211\u4eec\u73b0\u5728\u5c06\u89e3\u91ca\u6b64\u7c7b\u6982\u7387\u7684\u4e24\u4e2a\u793a\u4f8b\uff0c\u4ee5\u4fbf\u60a8\u66f4\u597d\u5730\u7406\u89e3\u5176\u542b\u4e49\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u629b\u4e00\u679a\u786c\u5e01\u548c\u4e00\u4e2a\u9ab0\u5b50<\/h3>\n<p>\u4f8b\u5982\uff0c\u629b\u786c\u5e01\u65f6\u5f97\u5230\u6b63\u9762\u7684\u6982\u7387\u662f 1\/2\uff0c\u800c\u629b\u9ab0\u5b50\u65f6\u5f97\u5230\u6570\u5b57 4 \u7684\u6982\u7387\u662f 1\/6\u3002\u56e0\u6b64\uff0c\u5f97\u5230\u6b63\u9762\u548c\u6570\u5b57 4 \u7684\u8054\u5408\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-fcbb87b4ec4d1525d162ea0499e6f632_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}P(A\\cap B)=P(A)\\cdot P(B)=\\\\[2ex] =\\cfrac{1}{2}\\cdot \\cfrac{1}{6}=\\cfrac{1}{12}=0,083\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"77\" width=\"212\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\">\u4e24\u6b21\u63b7\u9ab0\u5b50\u4e8b\u4ef6<\/h3>\n<p>\u6211\u4eec\u8fd8\u53ef\u4ee5\u4ece\u540c\u4e00\u4e2a\u968f\u673a\u5b9e\u9a8c\u4e2d\u627e\u5230\u4e24\u4e2a\u4e0d\u540c\u4e8b\u4ef6\u7684\u8054\u5408\u6982\u7387\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u8ba1\u7b97\u63b7\u9ab0\u5b50\u65f6<em>\u201c\u63b7\u51fa\u5947\u6570\u201d<\/em>\u548c<em>\u201c\u63b7\u51fa\u5927\u4e8e4\u7684\u6570\u5b57\u201d<\/em>\u4e8b\u4ef6\u540c\u65f6\u51fa\u73b0\u7684\u6982\u7387\u3002<\/p>\n<p>\u9ab0\u5b50\u4e0a\u6709\u4e09\u4e2a\u5947\u6570\uff081\u30013 \u548c 5\uff09\uff0c\u56e0\u6b64\u83b7\u5f97\u5947\u6570\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-8e7182c80426b8d6d491af6c679f0527_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A)=\\cfrac{3}{6}=0,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"124\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u9ab0\u5b50\u6709\u4e24\u4e2a\u5927\u4e8e\u56db\u7684\u6570\u5b57\uff085 \u548c 6\uff09\uff0c\u56e0\u6b64\u7b2c\u4e8c\u4e2a\u4e8b\u4ef6\u53d1\u751f\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-563300d3d19119cf838f3ce63d4bf789_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(B)=\\cfrac{2}{6}=0,33\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"135\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u8981\u8ba1\u7b97\u4e24\u4e2a\u4e8b\u4ef6\u7684\u8054\u5408\u6982\u7387\uff0c\u53ea\u9700\u5c06\u627e\u5230\u7684\u4e24\u4e2a\u6982\u7387\u76f8\u4e58\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-f06dbe6207ae2ea038fe6727f383b5f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}P(A\\cap B)=P(A)\\cdot P(B)=\\\\[2ex] =0,5\\cdot 0,33=0,167\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"212\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"probabilidad-conjunta-y-probabilidad-marginal\"><\/span>\u8054\u5408\u6982\u7387\u548c\u8fb9\u9645\u6982\u7387<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u8054\u5408\u6982\u7387\u548c\u8fb9\u9645\u6982\u7387\u4e4b\u95f4\u7684\u533a\u522b\u5728\u4e8e<\/strong>\uff0c\u8054\u5408\u6982\u7387\u662f\u6307\u4e24\u4e2a\u6216\u591a\u4e2a\u4e8b\u4ef6\u540c\u65f6\u53d1\u751f\u7684\u6982\u7387\uff0c\u800c\u8fb9\u9645\u6982\u7387\u662f\u603b\u4e8b\u4ef6\u7684\u5b50\u96c6\u53d1\u751f\u7684\u6982\u7387\u3002<\/p>\n<p>\u60f3\u8c61\u4e00\u4e0b\uff0c\u6211\u4eec\u505a\u4e86\u4e00\u4e2a\u5b9e\u9a8c\uff0c\u8fde\u7eed 21 \u5929\u8bb0\u5f55\u5f53\u5929\u65e9\u4e0a\u662f\u6674\u5929\u8fd8\u662f\u9634\u5929\uff0c\u4ee5\u53ca\u4e0b\u5348\u662f\u5426\u4e0b\u96e8\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\/exemple-de-probabilite-jointe-et-marginale.png\" alt=\"\u8054\u5408\u6982\u7387\u793a\u4f8b\" class=\"wp-image-595\" width=\"321\" height=\"155\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u4f8b\u5982\uff0c\u4e00\u5929\u4e3a\u9634\u5929\u7684\u8fb9\u9645\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-f4ff1a041ddd1850f21133f0ebfe8a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P(\\text{nublado})=\\cfrac{11}{21}=0,52\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"190\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u6709\u4e00\u5929\u4e0b\u96e8\u7684\u8fb9\u9645\u6982\u7387\u662f\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-bfe2f34568b77377b1c870c37a027fe6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P(\\text{llueve})=\\cfrac{9}{21}=0,43\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"174\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u7136\u800c\uff0c\u4e00\u5929\u9634\u5929\u548c\u96e8\u5929\u7684\u8054\u5408\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-a1f8a535c55fd3d92b114f7767b359fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P(\\text{nublado y llueve})=\\cfrac{7}{21}=0,33\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"256\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"probabilidad-conjunta-y-probabilidad-condicional\"><\/span>\u8054\u5408\u6982\u7387\u548c\u6761\u4ef6\u6982\u7387<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u53e6\u5916\u4e24\u4e2a\u7ecf\u5e38\u6df7\u6dc6\u7684\u6982\u5ff5\u662f\u8054\u5408\u6982\u7387\u548c\u6761\u4ef6\u6982\u7387\uff0c\u4f46\u5b83\u4eec\u7684\u542b\u4e49\u4e0d\u540c\u3002<\/p>\n<p><strong>\u8054\u5408\u6982\u7387\u548c\u6761\u4ef6\u6982\u7387\u4e4b\u95f4\u7684\u533a\u522b\u5728\u4e8e<\/strong>\uff0c\u8054\u5408\u6982\u7387\u4e2d\u4e24\u4e2a\u4e8b\u4ef6\u5fc5\u987b\u540c\u65f6\u53d1\u751f\uff0c\u800c\u6761\u4ef6\u6982\u7387\u662f\u6307\u5982\u679c\u53e6\u4e00\u4e2a\u4e8b\u4ef6\u53d1\u751f\u5219\u4e00\u4e2a\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\u3002\u5df2\u7ecf\u751f\u4ea7\u4e86\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\/exemple-de-probabilite-jointe-et-marginale.png\" alt=\"\u8054\u5408\u6982\u7387\u548c\u6761\u4ef6\u6982\u7387\u7684\u793a\u4f8b\" class=\"wp-image-595\" width=\"321\" height=\"155\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u901a\u8fc7\u91cd\u590d\u4e0e\u4e4b\u524d\u76f8\u540c\u7684\u7ec3\u4e60\uff0c\u4e00\u5929\u9634\u5929\u548c\u96e8\u5929\u7684\u8054\u5408\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-a1f8a535c55fd3d92b114f7767b359fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P(\\text{nublado y llueve})=\\cfrac{7}{21}=0,33\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"256\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u4f46\u662f\uff0c\u5047\u8bbe\u67d0\u5929\u662f\u9634\u5929\uff0c\u67d0\u5929\u4f1a\u4e0b\u96e8\u7684\u6761\u4ef6\uff08\u6216\u6709\u6761\u4ef6\uff09\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-8481ae94675947936a45242e56c45365_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P(\\text{llueve }|\\text{ nublado})=\\cfrac{7}{11}=0,64\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"252\" style=\"vertical-align: 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