{"id":391,"date":"2023-08-01T06:26:21","date_gmt":"2023-08-01T06:26:21","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%a6%82%e7%8e%87%e8%ae%a1%e7%ae%97\/"},"modified":"2023-08-01T06:26:21","modified_gmt":"2023-08-01T06:26:21","slug":"%e6%a6%82%e7%8e%87%e8%ae%a1%e7%ae%97","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%a6%82%e7%8e%87%e8%ae%a1%e7%ae%97\/","title":{"rendered":"\u6982\u7387\u8ba1\u7b97"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u5982\u4f55\u8ba1\u7b97\u4e8b\u4ef6\u6982\u7387\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u627e\u5230\u8ba1\u7b97\u6982\u7387\u7684\u516c\u5f0f\u3001\u6982\u7387\u8ba1\u7b97\u7684\u793a\u4f8b\uff0c\u6b64\u5916\u8fd8\u6709\u4e00\u4e2a\u7528\u4e8e\u8ba1\u7b97\u4efb\u4f55\u4e8b\u4ef6\u6982\u7387\u7684\u5728\u7ebf\u8ba1\u7b97\u5668\u3002<\/p>\n<p>\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u6982\u7387\u8ba1\u7b97\u6709\u5f88\u591a\u5e94\u7528\uff0c\u4f8b\u5982\uff0c\u5b83\u53ef\u4ee5\u7528\u6765\u8ba1\u7b97\u4e00\u9879\u6295\u8d44\u6210\u529f\u7684\u6982\u7387\u3001\u6709\u4e00\u5929\u4e0b\u96e8\u7684\u6982\u7387\u3001\u4e00\u4e2a\u4eba\u60a3\u67d0\u79cd\u75be\u75c5\u7684\u6982\u7387\u3002\u67d0\u4e9b\u75c7\u72b6\u7b49<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-calculo-de-probabilidades\"><\/span>\u6982\u7387\u8ba1\u7b97\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8981\u8ba1\u7b97\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\uff0c\u5fc5\u987b\u5c06\u6709\u5229\u4e8b\u4f8b\u7684\u6570\u91cf\u9664\u4ee5\u53ef\u80fd\u4e8b\u4f8b\u7684\u6570\u91cf\u3002\u56e0\u6b64\uff0c<strong>\u6982\u7387\u8ba1\u7b97\u516c\u5f0f<\/strong>\u4e3a\uff1a\u6982\u7387=\u6709\u5229\u6848\u4f8b\/\u53ef\u80fd\u6848\u4f8b\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-d3b5a3fd8897ec1933cfc654566b84dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A)=\\cfrac{\\text{casos favorables}}{\\text{casos posibles}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"190\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:10px\">\u91d1\u5b50\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:10px\"> <span style=\"color:#101010;font-weight: normal;\">P(A) \u662f\u4e8b\u4ef6 A \u7684\u6982\u7387\u3002<\/span><\/li>\n<li style=\"margin-bottom:10px\"><span style=\"color:#101010;font-weight: normal;\">\u6709\u5229\u7684\u60c5\u51b5\u662f\u6ee1\u8db3\u76f8\u5173\u4e8b\u4ef6\u6761\u4ef6\u7684\u6240\u6709\u7ed3\u679c\u3002<\/span><\/li>\n<li style=\"margin-bottom:10px\"><span style=\"color:#101010;font-weight: normal;\">\u53ef\u80fd\u7684\u60c5\u51b5\u662f\u53ef\u80fd\u53d1\u751f\u7684\u7ed3\u679c\u7684\u603b\u6570\u3002<\/span><\/li>\n<\/ul>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u6982\u7387\u503c\u662f 0 \u5230 1 \u4e4b\u95f4\u7684\u6570\u5b57\u3002\u6982\u7387\u8d8a\u9ad8\uff0c\u4e8b\u4ef6\u53d1\u751f\u7684\u53ef\u80fd\u6027\u5c31\u8d8a\u5927\u3002\u56e0\u6b64\uff0c\u6982\u7387\u4e3a 0 \u610f\u5473\u7740\u8be5\u4e8b\u4ef6\u4e0d\u4f1a\u53d1\u751f\uff0c\u800c\u6982\u7387\u4e3a 1 \u610f\u5473\u7740\u8be5\u4e8b\u4ef6\u603b\u662f\u4f1a\u53d1\u751f\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u8981\u8ba1\u7b97\u629b\u786c\u5e01\u65f6\u6b63\u9762\u671d\u4e0a\u7684\u6982\u7387\uff0c\u5fc5\u987b\u5c06\u6709\u5229\u60c5\u51b5\u7684\u6570\u91cf (1) \u9664\u4ee5\u53ef\u80fd\u60c5\u51b5\u7684\u6570\u91cf (2)\u3002\u56e0\u6b64\uff0c\u83b7\u5f97\u6b63\u9762\u7684\u6982\u7387\u4e3a 1\/2 = 0.50\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-12569f67a825f820238af78b037352f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{cara})=\\cfrac{\\text{casos favorables}}{\\text{casos posibles}}=\\cfrac{1}{2}=0,50\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"301\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\u4e5f\u53ef\u4ee5\u7528\u767e\u5206\u6bd4\u8868\u793a\uff0c\u53ea\u9700\u5c06\u7ed3\u679c\u4e58\u4ee5 100\u3002<\/p>\n<p>\u8fd9\u4e2a\u5141\u8bb8\u6211\u4eec\u8ba1\u7b97\u7edd\u5927\u591a\u6570\u4e8b\u4ef6\u6982\u7387\u7684\u516c\u5f0f\u88ab\u79f0\u4e3a\u62c9\u666e\u62c9\u65af\u6cd5\u5219\uff0c\u4ee5\u7eaa\u5ff5\u6570\u5b66\u5bb6\u76ae\u57c3\u5c14-\u897f\u8499\u00b7\u62c9\u666e\u62c9\u65af\uff08Pierre-Simon Laplace\uff0c1749-1827\uff09\uff0c\u4ed6\u5960\u5b9a\u4e86\u6982\u7387\u8bba\u7684\u57fa\u7840\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=\"ejemplos-de-calculos-de-probabilidades\"><\/span>\u6982\u7387\u8ba1\u7b97\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u5df2\u7ecf\u4e86\u89e3\u4e86\u4ec0\u4e48\u662f\u6982\u7387\u8ba1\u7b97\uff0c\u4e0b\u9762\u662f\u5982\u4f55\u8ba1\u7b97\u4e0d\u540c\u4e8b\u4ef6\u7684\u6982\u7387\u7684\u51e0\u4e2a\u793a\u4f8b\uff0c\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u8fd9\u4e2a\u6982\u5ff5\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-lanzamiento-de-un-dado\"><\/span>\u793a\u4f8b 1\uff1a\u63b7\u9ab0\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>\u63b7\u9ab0\u5b50\u5f97\u5230\u5076\u6570\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f<\/li>\n<\/ul>\n<p>\u4e3a\u4e86\u627e\u5230\u4e8b\u4ef6\u7684\u6982\u7387\uff0c\u6211\u4eec\u9700\u8981\u5e94\u7528\u4e0a\u9762\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-d3b5a3fd8897ec1933cfc654566b84dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A)=\\cfrac{\\text{casos favorables}}{\\text{casos posibles}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"190\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6709\u5229\u60c5\u51b5\u7684\u6570\u91cf\u4e3a 3\uff0c\u56e0\u4e3a\u9ab0\u5b50\u4e0a\u6709 3 \u4e2a\u5076\u6570\uff082\u30014\u30016\uff09\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u53ef\u80fd\u60c5\u51b5\u7684\u6570\u91cf\u7b49\u4e8e\u6240\u6709\u53ef\u80fd\u7ed3\u679c\uff0c\u5373 6\uff0c\u56e0\u4e3a\u9ab0\u5b50\u6709\u516d\u4e2a\u9762\uff081\u30012\u30013\u30014\u30015\u30016\uff09\u3002\u56e0\u6b64\u7ec3\u4e60\u8981\u6c42\u6211\u4eec\u505a\u7684\u4e8b\u4ef6\u7684\u6982\u7387\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-6122d4de7d9271015aede4a33b6862a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{n\\'umero par})=\\cfrac{3}{6}=0,50\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"210\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u63b7\u9ab0\u5b50\u65f6\u63b7\u51fa\u5076\u6570\u7684\u6982\u7387\u4e3a 0.50\uff0c\u5373 50%\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-bolas-de-una-bolsa\"><\/span>\u793a\u4f8b 2\uff1a\u888b\u5b50\u4e2d\u7684\u7403<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>\u5728\u4e00\u4e2a\u7a7a\u76d2\u5b50\u91cc\uff0c\u6211\u4eec\u653e\u4e86 5 \u4e2a\u84dd\u7403\u30014 \u4e2a\u7eff\u7403\u548c 2 \u4e2a\u9ec4\u7403\u3002\u5f53\u4f60\u968f\u673a\u62bd\u53d6\u4e00\u4e2a\u7403\u65f6\uff0c\u5b83\u662f\u84dd\u8272\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f<\/li>\n<\/ul>\n<p>\u4e3a\u4e86\u786e\u5b9a\u4e8b\u4ef6\u7684\u6982\u7387\uff0c\u6211\u4eec\u5fc5\u987b\u5e94\u7528\u6587\u7ae0\u5f00\u5934\u89e3\u91ca\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-d3b5a3fd8897ec1933cfc654566b84dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A)=\\cfrac{\\text{casos favorables}}{\\text{casos posibles}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"190\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u5728\u672c\u4f8b\u4e2d\uff0c\u6709\u5229\u6848\u4f8b\u7684\u6570\u91cf\u4e3a 5\uff0c\u56e0\u4e3a\u6211\u4eec\u5728\u6846\u4e2d\u653e\u5165\u4e86 5 \u4e2a\u84dd\u8272\u7403\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u53ef\u80fd\u7684\u76d2\u5b50\u6570\u91cf\u662f\u6240\u6709\u653e\u7f6e\u7684\u7403\u7684\u603b\u548c\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-613fe8177cd01f9796d49b5ea92590c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{bola azul})=\\cfrac{5}{5+4+2}=\\cfrac{5}{11}=0,45\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"294\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u4ece\u76d2\u5b50\u4e2d\u62bd\u51fa\u84dd\u8272\u7403\u7684\u6982\u7387\u4e3a 0.45\uff0c\u6216\u8005\u4ee5\u767e\u5206\u6bd4\u8868\u793a\u4e3a 45%\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\/\u6982\u7387\u7684\u7c7b\u578b\/\">\u6982\u7387\u7c7b\u578b<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-de-probabilidades\"><\/span>\u8d54\u7387\u8ba1\u7b97\u5668<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5c06\u6709\u5229\u6848\u4f8b\u6570\u548c\u53ef\u80fd\u6848\u4f8b\u6570\u8f93\u5165\u5230\u4e0b\u9762\u7684\u8ba1\u7b97\u5668\u4e2d\uff0c\u8ba1\u7b97\u8be5\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\u3002<\/p>\n<form action=\"\" method=\"post\">\n<div style=\"margin-bottom:20px; margin-left:5%\"> <span style=\"color:#101010;font-weight: normal;\"><span style=\"color:#1C2C92\"><strong>\u27a4<\/strong><\/span>\u6709\u5229\u6848\u4f8b\u6570\u91cf\uff1a <input name=\"casosfavorables\" style=\"border:1.5px solid #4FC3F7; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce el n\u00famero de casos favorables aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/span><\/div>\n<div style=\"margin-bottom:20px; margin-left:5%\"> <span style=\"color:#101010;font-weight: normal;\"><span style=\"color:#1C2C92\"><strong>\u27a4<\/strong><\/span>\u53ef\u80fd\u60c5\u51b5\u7684\u6570\u91cf\uff1a <input name=\"casosposibles\" style=\"border:1.5px solid #4FC3F7; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce el n\u00famero de casos posibles aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/span> <\/div>\n<div style=\"text-align:center\"><input align=\"center\" style=\"border-radius:30px; margin: 20px\" type=\"submit\" name=\"submit\" value=\"\u8ba1\u7b97\u6982\u7387\"><\/div>\n<\/form>\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\/\u6982\u7387\u516c\u5f0f\/\">\u6982\u7387\u516c\u5f0f<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculo-de-la-probabilidad-condicionada\"><\/span>\u6761\u4ef6\u6982\u7387\u8ba1\u7b97<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6761\u4ef6\u6982\u7387\uff0c\u4e5f\u79f0\u4e3a\u6761\u4ef6\u6982\u7387\uff0c\u8868\u793a\u5982\u679c\u53e6\u4e00\u4e2a\u4e8b\u4ef6 B \u53d1\u751f\uff0c\u4e8b\u4ef6 A \u4e5f\u5c06\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>\u56e0\u6b64\uff0c\u4e8b\u4ef6 A \u7ed9\u5b9a\u4e8b\u4ef6 B \u7684\u6761\u4ef6\u6982\u7387\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<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f95773f97f65355e94817757e7bc3e76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A|B)=\\cfrac{P(A\\cap B)}{P(B)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"161\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u60a8\u53ef\u4ee5\u5728\u6b64\u5904\u67e5\u770b\u5982\u4f55\u8ba1\u7b97\u4e8b\u4ef6\u7684\u6761\u4ef6\u6982\u7387\u7684\u793a\u4f8b\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 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