{"id":14350,"date":"2024-03-17T23:03:54","date_gmt":"2024-03-17T15:03:54","guid":{"rendered":"https:\/\/blog.iyatt.com\/?p=14350"},"modified":"2025-08-21T20:39:29","modified_gmt":"2025-08-21T12:39:29","slug":"%e6%95%b0%e5%ad%a6%e4%b8%8e%e8%ae%a1%e7%ae%97%e6%9c%ba%ef%bc%883%ef%bc%89-%e6%a6%82%e7%8e%87%e8%ae%ba%ef%bc%88%e7%bc%96%e8%be%91%e4%b8%ad%ef%bc%89","status":"publish","type":"post","link":"https:\/\/blog.iyatt.com\/?p=14350","title":{"rendered":"\u6570\u5b66\u4e0e\u8ba1\u7b97\u673a\u3010\u6982\u7387\u8bba\u3011"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 ez-toc-wrap-center counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">\u76ee\u5f55<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/blog.iyatt.com\/?p=14350\/#1_%E9%9A%8F%E6%9C%BA%E4%BA%8B%E4%BB%B6\" >1 \u968f\u673a\u4e8b\u4ef6<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/blog.iyatt.com\/?p=14350\/#11_%E4%BA%8B%E4%BB%B6%E9%97%B4%E7%9A%84%E5%85%B3%E7%B3%BB%E4%B8%8E%E8%BF%90%E7%AE%97\" >1.1 \u4e8b\u4ef6\u95f4\u7684\u5173\u7cfb\u4e0e\u8fd0\u7b97<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/blog.iyatt.com\/?p=14350\/#12_%E6%A6%82%E7%8E%87%E5%92%8C%E9%A2%91%E7%8E%87\" >1.2 \u6982\u7387\u548c\u9891\u7387<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/blog.iyatt.com\/?p=14350\/#%E4%BE%8B%E4%B8%80\" >\u4f8b\u4e00<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/blog.iyatt.com\/?p=14350\/#13_%E5%8F%A4%E5%85%B8%E6%A6%82%E5%9E%8B\" >1.3 \u53e4\u5178\u6982\u578b<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/blog.iyatt.com\/?p=14350\/#2_%E6%9D%A1%E4%BB%B6%E6%A6%82%E7%8E%87\" >2 \u6761\u4ef6\u6982\u7387<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/blog.iyatt.com\/?p=14350\/#%E4%BE%8B%E4%B8%80-2\" >\u4f8b\u4e00<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/blog.iyatt.com\/?p=14350\/#%E4%BE%8B%E4%BA%8C\" >\u4f8b\u4e8c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/blog.iyatt.com\/?p=14350\/#21_%E4%BA%8B%E4%BB%B6%E7%8B%AC%E7%AB%8B%E6%80%A7\" >2.1 \u4e8b\u4ef6\u72ec\u7acb\u6027<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/blog.iyatt.com\/?p=14350\/#%E4%BE%8B%E4%B8%80-3\" >\u4f8b\u4e00<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/blog.iyatt.com\/?p=14350\/#22_%E7%8B%AC%E7%AB%8B%E8%AF%95%E9%AA%8C\" >2.2 \u72ec\u7acb\u8bd5\u9a8c<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/blog.iyatt.com\/?p=14350\/#%E4%BE%8B%E4%B8%80-4\" >\u4f8b\u4e00<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h1><span class=\"ez-toc-section\" id=\"1_%E9%9A%8F%E6%9C%BA%E4%BA%8B%E4%BB%B6\"><\/span>1 \u968f\u673a\u4e8b\u4ef6<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p><strong>\u968f\u673a\u4e8b\u4ef6<\/strong>\u6ee1\u8db3\u7684\u7279\u5f81\uff1a<\/p>\n<ul>\n<li>\u53ef\u4ee5\u5728\u60f3\u7528\u6761\u4ef6\u4e0b\u91cd\u590d\u6267\u884c<\/li>\n<li>\u4e8b\u5148\u53ef\u77e5\u53ef\u80fd\u51fa\u73b0\u7684\u7ed3\u679c<\/li>\n<li>\u8bd5\u9a8c\u5f00\u59cb\u524d\u4e0d\u786e\u5b9a\u5f53\u6b21\u7684\u7ed3\u679c<\/li>\n<\/ul>\n<p>\u968f\u673a\u8bd5\u9a8c\u4e2d\u6bcf\u4e00\u4e2a\u53ef\u80fd\u51fa\u73b0\u7684\u8bd5\u9a8c\u7ed3\u679c\u79f0\u4e3a\u4e00\u4e2a\u6837\u672c\u70b9\uff0c\u8bb0\u4f5c<code class=\"katex-inline\">\\omega<\/code>\uff0c\u6240\u6709\u53ef\u80fd\u51fa\u73b0\u7684\u8bd5\u9a8c\u7ed3\u679c\u7ec4\u6210\u7684\u96c6\u5408\u79f0\u4e3a<strong>\u6837\u672c\u7a7a\u95f4<\/strong>\uff0c\u8bb0\u4e3a<code class=\"katex-inline\">\\Omega<\/code>\uff0c\u5373<code class=\"katex-inline\">\\Omega=\\{\\omega_1,\\omega_2,\\cdots,\\omega_n\\}<\/code><\/p>\n<h2><span class=\"ez-toc-section\" id=\"11_%E4%BA%8B%E4%BB%B6%E9%97%B4%E7%9A%84%E5%85%B3%E7%B3%BB%E4%B8%8E%E8%BF%90%E7%AE%97\"><\/span>1.1 \u4e8b\u4ef6\u95f4\u7684\u5173\u7cfb\u4e0e\u8fd0\u7b97<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<pre><code class=\"language-katex\">\\begin{array}{|l|l|l|}\n\\hline\n\u8bb0\u53f7 &amp; \u6982\u7387\u8bba &amp; \u96c6\u5408\u8bba \\\\\n\\hline\n\\Omega &amp; \u6837\u672c\u7a7a\u95f4\uff0c\u5fc5\u7136\u4e8b\u4ef6 &amp; \u5168\u96c6 \\\\\n\\hline\n\\emptyset &amp; \u4e0d\u53ef\u80fd\u4e8b\u4ef6 &amp; \u7a7a\u96c6 \\\\\n\\hline\n\\omega &amp; \u57fa\u672c\u4e8b\u4ef6 &amp; \u5143\u7d20 \\\\\n\\hline\nA &amp; \u4e8b\u4ef6 &amp; \u5b50\u96c6 \\\\\n\\hline\n\\overline{A} &amp; \u4e8b\u4ef6A\u7684\u5bf9\u7acb\u4e8b\u4ef6 &amp; A\u7684\u4f59\u96c6 \\\\\n\\hline\nA\\subset B &amp; \u4e8b\u4ef6A\u53d1\u751f\u5bfc\u81f4\u4e8b\u4ef6B\u53d1\u751f &amp; A\u662fB\u7684\u5b50\u96c6 \\\\\n\\hline\nA=B &amp; \u4e8b\u4ef6A\u4e0e\u4e8b\u4ef6B\u76f8\u7b49 &amp; A\u4e0eB\u76f8\u7b49 \\\\\n\\hline\nA\\cup B &amp; \u4e8b\u4ef6A\u4e0e\u4e8b\u4ef6B\u81f3\u5c11\u6709\u4e00\u4e2a\u53d1\u751f &amp; A\u4e0eB\u7684\u5e76\u96c6 \\\\\n\\hline\nA\\cap B\u6216AB &amp; \u4e8b\u4ef6A\u4e0e\u4e8b\u4ef6B\u540c\u65f6\u53d1\u751f &amp; A\u4e0eB\u7684\u4ea4\u96c6 \\\\\n\\hline\nA-B &amp; \u4e8b\u4ef6A\u53d1\u751f\u800c\u4e8b\u4ef6B\u4e0d\u53d1\u751f &amp; A\u4e0eB\u7684\u5dee\u96c6 \\\\\n\\hline\nAB=\\varnothing &amp; \u4e8b\u4ef6A\u4e0e\u4e8b\u4ef6B\u4e92\u4e0d\u76f8\u5bb9 &amp; A\u4e0eB\u6ca1\u6709\u76f8\u540c\u7684\u5143\u7d20 \\\\\n\\hline\n\\end{array}<\/code><\/pre>\n<p>\u4e8b\u4ef6\u7684\u8fd0\u7b97\u5b9a\u5f8b<br \/>\n\u5e42\u7b49\u5f8b\uff1a<code class=\"katex-inline\">A\\cup A=A<\/code>\uff0c<code class=\"katex-inline\">A\\cap A=A<\/code><br \/>\n\u4ea4\u6362\u5f8b\uff1a<code class=\"katex-inline\">A\\cup B=B\\cup A<\/code>\uff0c<code class=\"katex-inline\">A\\cap B=B\\cap A<\/code><br \/>\n\u7ed3\u5408\u5f8b\uff1a<code class=\"katex-inline\">(A\\cup B)\\cup C=A\\cup(B\\cup C)<\/code>\uff0c<code class=\"katex-inline\">(A\\cap B)\\cap C=A\\cap(B\\cap C)<\/code><br \/>\n\u5206\u914d\u5f8b\uff1a<code class=\"katex-inline\">A\\cap(B\\cup C)=(A\\cap B)\\cup(A\\cap C)<\/code>\uff0c<code class=\"katex-inline\">A\\cup(B\\cap C)=(A\\cup B)\\cap(A\\cup B)<\/code><br \/>\n\u5fb7\u6469\u6839\u7387\uff1a<code class=\"katex-inline\">\\overline{A\\cup B}=\\overline A\\cap\\overline B<\/code>\uff0c<code class=\"katex-inline\">\\overline{A\\cap B}=\\overline A\\cup\\overline B<\/code><\/p>\n<h2><span class=\"ez-toc-section\" id=\"12_%E6%A6%82%E7%8E%87%E5%92%8C%E9%A2%91%E7%8E%87\"><\/span>1.2 \u6982\u7387\u548c\u9891\u7387<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6982\u7387\u5b9a\u4e49\uff1a\u968f\u673a\u4e8b\u4ef6A\u5728n\u6b21\u8bd5\u9a8c\u4e2d\u53d1\u751f\u7684\u9891\u7387\u4e3a<code class=\"katex-inline\">f_n(A)=\\frac{n_A}{n}<\/code>\uff0c\u5176\u4e2d<code class=\"katex-inline\">n_A<\/code>\u662fA\u53d1\u751f\u7684\u6b21\u6570\uff08\u9891\u6570\uff09\uff0cn\u662f\u603b\u8bd5\u9a8c\u6b21\u6570\u3002\u968f\u7740\u8bd5\u9a8c\u6b21\u6570\u7684\u589e\u591a\uff0c<code class=\"katex-inline\">f_n(A)<\/code>\u8d8b\u4e8e\u7a33\u5b9a\u503cp\uff0c\u79f0\u968f\u673a\u4e8b\u4ef6A\u7684\u6982\u7387\u4e3aP(A)=p\u3002<\/p>\n<p>\u6982\u7387\u7279\u6027\uff1a<br \/>\n\u975e\u8d1f\u6027\uff1a\u5bf9\u4efb\u610f\u7684\u968f\u673a\u4e8b\u4ef6A\uff0cP(A)<code class=\"katex-inline\">\\ge<\/code>0<br \/>\n\u89c4\u8303\u6027\uff1a<code class=\"katex-inline\">P(\\Omega)=1<\/code><br \/>\n\u53ef\u52a0\u6027\uff1a\u5bf9\u4e8eN\u4e2a\u4e92\u65a5\u7684\u4e8b\u4ef6A\uff0c<code class=\"katex-inline\">i=1,\\cdots,N<\/code>\uff0c\u5176\u548c\u4e8b\u4ef6\u7684\u6982\u7387\u5e94\u8be5\u7b49\u4e8e\u5b83\u4eec\u7684\u6982\u7387\u4e4b\u548c\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E4%BE%8B%E4%B8%80\"><\/span>\u4f8b\u4e00<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u4e0b\u9762\u5199\u4e00\u4e2a\u7a0b\u5e8f\u6a21\u62df\u786c\u5e01\u629b\u63b7\uff0c\u4ece 0 \u548c 1 \u4e2d\u968f\u673a\u53d6\u4e00\u4e2a\uff0c0 \u4ee3\u8868\u6b63\u9762\uff0c\u7edf\u8ba1\u51fa\u73b0 0 \u7684\u6b21\u6570\uff0c\u518d\u548c\u8bd5\u9a8c\u6b21\u6570\u6bd4\u8d77\u6765\u8ba1\u7b97\u6b63\u9762\u51fa\u73b0\u7684\u9891\u7387\u3002<\/p>\n<pre><code class=\"language-py\">import random\n\ndef coin_trial(times):\n    heads = 0\n    for i in range(times):\n        if random.randint(0, 1) == 0:\n            print\n            heads += 1\n    return heads\n\ndef simulate(times):\n    return coin_trial(times) \/ times\n\nprint(simulate(10))\nprint(simulate(100))\nprint(simulate(1000))\nprint(simulate(10000))\nprint(simulate(100000))\nprint(simulate(1000000))<\/code><\/pre>\n<p>\u5728\u8bd5\u9a8c\u6b21\u6570\u4e3a 10 \u65f6\u7ed3\u679c\u7ecf\u5e38\u504f\u5dee\u5f88\u5927\uff0c\u65f6\u9ad8\u65f6\u4f4e\uff0c\u5f53\u6b21\u6570\u589e\u5927\u5230\u4e00\u5b9a\u5c42\u5ea6\u540e\uff0c\u7ed3\u679c\u5c31\u7a33\u5b9a\u8d8b\u5411 0.5 \u4e86\u3002<br \/>\n<img decoding=\"async\" data-src=\"https:\/\/blog.iyatt.com\/wp-content\/uploads\/2024\/03\/image-1710727321232.png\" alt=\"file\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" style=\"--smush-placeholder-width: 90px; --smush-placeholder-aspect-ratio: 90\/126;\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"13_%E5%8F%A4%E5%85%B8%E6%A6%82%E5%9E%8B\"><\/span>1.3 \u53e4\u5178\u6982\u578b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u53e4\u5178\u6982\u578b\u4e2d\u6837\u672c\u7a7a\u95f4\u53ea\u6709\u6709\u9650\u4e2a\u6837\u672c\u70b9\uff0c\u5e76\u4e14\u6bcf\u4e2a\u6837\u672c\u70b9\u6784\u6210\u7684\u57fa\u672c\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\u662f\u76f8\u540c\u7684\uff0c\u56e0\u6b64\u53e4\u5178\u6982\u578b\u53c8\u79f0\u4e3a\u7b49\u53ef\u80fd\u6982\u578b\u3002<br \/>\n\u5b9a\u4e49\uff1a\u6837\u672c\u7a7a\u95f4<code class=\"katex-inline\">\\Omega=\\{\\omega_1,\\omega_2,\\cdots,\\omega_n\\}<\/code>\uff0c<code class=\"katex-inline\">P(\\{\\omega_i\\})=\\frac{1}{n}<\/code>\uff0c<code class=\"katex-inline\">i=1,2,3,\\cdots,n<\/code>\u3002<\/p>\n<h1><span class=\"ez-toc-section\" id=\"2_%E6%9D%A1%E4%BB%B6%E6%A6%82%E7%8E%87\"><\/span>2 \u6761\u4ef6\u6982\u7387<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p>\u8bbeA\u3001B\u4e3a\u968f\u673a\u4e8b\u4ef6\uff0c\u4e14P(A)&gt;0\uff0c\u5219\u6709<br \/>\n<code class=\"katex-inline\">P(B|A)=\\frac{P(AB)}{P(A)}<\/code><br \/>\n\u79f0P(B|A)\u4e3a\u5728\u4e8b\u4ef6A\u53d1\u751f\u7684\u6761\u4ef6\u4e0b\uff0c\u4e8b\u4ef6B\u53d1\u751f\u7684\u6982\u7387\u3002<\/p>\n<p>\u7ed3\u5408\u56fe\u7247\u6765\u7406\u89e3\uff0cA\u662f\u5de6\u8fb9\u7684\u5706\uff0cB\u662f\u53f3\u8fb9\u7684\u5706\uff0cC\u662fA\u548cB\u7684\u516c\u5171\u90e8\u5206\uff0c\u5373<code class=\"katex-inline\">C=AB=A\\cap B<\/code>\u3002<br \/>\n(B|A)\u5c31\u662f\u5728A\u53d1\u751f\u7684\u60c5\u51b5\u4e0b\uff0cC\u53d1\u751f\u7684\u6982\u7387\uff0c\u5373<code class=\"katex-inline\">P(B|A)=\\frac{\\frac{n(AB)}{n(\\Omega)}}{\\frac{n(A)}{n(\\Omega)}}=\\frac{n(C)}{n(A)}<\/code><br \/>\n<img decoding=\"async\" data-src=\"https:\/\/blog.iyatt.com\/wp-content\/uploads\/2024\/03\/image-1710984963419.png\" alt=\"file\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" style=\"--smush-placeholder-width: 667px; --smush-placeholder-aspect-ratio: 667\/424;\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E4%BE%8B%E4%B8%80-2\"><\/span>\u4f8b\u4e00<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u67d0\u5382\u751f\u4ea7\u7684\u4ea7\u54c1\u80fd\u76f4\u63a5\u51fa\u5382\u7684\u6982\u7387\u4e3a 70%\uff0c\u4f59\u4e0b\u7684 30% \u7684\u4ea7\u54c1\u8981\u8c03\u8bd5\u540e\u518d\u5b9a\u3002\u5df2\u77e5\u8c03\u8bd5\u540e\u6709 80% \u7684\u4ea7\u54c1\u53ef\u4ee5\u51fa\u5382\uff0c20% \u7684\u4ea7\u54c1\u8981\u62a5\u5e9f\uff0c\u6c42\u8be5\u5382\u4ea7\u54c1\u7684\u62a5\u5e9f\u7387\u3002<\/p>\n<p>\u8bbe A \u4e3a\u6700\u7ec8\u90fd\u53ef\u4ee5\u51fa\u5382\u7684\uff0c\u8bbe B \u4e3a\u8981\u8c03\u8bd5\u7684\u3002A \u5206\u4e3a\u53ef\u4ee5\u76f4\u63a5\u51fa\u5382\u7684\u548c\u9700\u8981\u8c03\u8bd5\u540e\u624d\u80fd\u51fa\u5382\u7684\u4e24\u90e8\u5206\uff0cB \u5206\u4e3a\u8c03\u8bd5\u540e\u53ef\u4ee5\u51fa\u5382\u7684\u548c\u8c03\u8bd5\u540e\u62a5\u5e9f\u7684\u4e24\u90e8\u5206\uff0c\u62a5\u5e9f\u7684\u53ea\u6765\u6e90\u4e8e\u8c03\u8bd5\u540e\u62a5\u5e9f\u7684\uff0c\u8c03\u8bd5\u540e\u62a5\u5e9f\u7684\u5360\u8c03\u8bd5\u7684 20%\uff0c\u8c03\u8bd5\u7684\u5360\u603b\u7684 30%\uff0c\u90a3\u4e48P(\u8c03\u8bd5\u540e\u62a5\u5e9f)=30% x 20%=6%\u3002<br \/>\n<img decoding=\"async\" data-src=\"https:\/\/blog.iyatt.com\/wp-content\/uploads\/2024\/03\/image-1710986080491.png\" alt=\"file\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" style=\"--smush-placeholder-width: 545px; --smush-placeholder-aspect-ratio: 545\/405;\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E4%BE%8B%E4%BA%8C\"><\/span>\u4f8b\u4e8c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7532\u4e59\u4e24\u5730\u96e8\u5929\u7684\u6982\u7387\u5206\u522b\u4e3a20%\u548c18%\uff0c\u4e24\u5730\u540c\u65f6\u4e0b\u96e8\u7684\u6982\u7387\u4e3a12%\uff0c\u8ba1\u7b97\uff1a<br \/>\n\uff081\uff09\u4e59\u4e3a\u96e8\u5929\uff0c\u7532\u4e3a\u96e8\u5929\u7684\u6982\u7387\u3002<br \/>\n\uff082\uff09\u7532\u4e3a\u96e8\u5929\uff0c\u4e59\u4e3a\u96e8\u5929\u7684\u6982\u7387\u3002<\/p>\n<p>\u8bbe A={\u7532\u4e3a\u96e8\u5929}\uff0cB={\u4e59\u4e3a\u96e8\u5929}<br \/>\n\u5219P(A)=0.2\uff0cP(B)=0.18\uff0cP(AB)=0.12<br \/>\n<img decoding=\"async\" data-src=\"https:\/\/blog.iyatt.com\/wp-content\/uploads\/2024\/03\/image-1710987480461.png\" alt=\"file\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" style=\"--smush-placeholder-width: 588px; --smush-placeholder-aspect-ratio: 588\/427;\" \/><\/p>\n<p>\u7b54\uff081\uff09<br \/>\n<code class=\"katex-inline\">P(A|B)=\\frac{P(AB)}{P(B)}=\\frac{0.12}{0.18}=\\frac{2}{3}<\/code><\/p>\n<p>\u7b54\uff082\uff09<br \/>\n<code class=\"katex-inline\">P(B|A)=\\frac{P(AB)}{P(A)}=\\frac{0.12}{0.2}=\\frac{3}{5}<\/code><\/p>\n<h2><span class=\"ez-toc-section\" id=\"21_%E4%BA%8B%E4%BB%B6%E7%8B%AC%E7%AB%8B%E6%80%A7\"><\/span>2.1 \u4e8b\u4ef6\u72ec\u7acb\u6027<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u968f\u673a\u4e8b\u4ef6\u4e4b\u95f4\u4e92\u76f8\u72ec\u7acb\uff0c\u4e0d\u4f1a\u5f71\u54cd\u3002\u6bd4\u5982\u6295\u63b7\u4e00\u679a\u786c\u5e01\uff0c\u8bbe\u7b2c\u4e00\u6b21\u4e3a\u6b63\u9762\u4e3a\u4e8b\u4ef6 A\uff0c\u7b2c\u4e8c\u6b21\u4e3a\u6b63\u9762\u4e3a\u4e8b\u4ef6 B\u3002\u95ee\u6295\u63b7\u4e24\u6b21\uff0c\u7b2c\u4e00\u6b21\u4e3a\u6b63\u9762\u7684\u60c5\u51b5\u4e0b\uff0c\u7b2c\u4e8c\u6b21\u4e5f\u4e3a\u6b63\u9762\u7684\u6982\u7387\uff0c\u4f1a\u53d1\u73b0\u7b2c\u4e00\u6b21\u7684\u7ed3\u679c\u5b8c\u5168\u4e0d\u4f1a\u5f71\u54cd\u7b2c\u4e8c\u6b21\u7684\u7ed3\u679c\uff0c\u4e0d\u7ba1\u7b2c\u4e00\u6b21\u7ed3\u679c\u662f\u6b63\u9762\u8fd8\u662f\u53cd\u9762\uff0c\u7b2c\u4e8c\u6b21\u7684\u4e3a\u6b63\u9762\u7684\u6982\u7387\u8fd8\u662f 0.5\u3002\u5219\u6709<br \/>\n<code class=\"katex-inline\">P(B|A)=\\frac{P(AB)}{P(A)}=P(B)<\/code><br \/>\n<code class=\"katex-inline\">P(AB)=P(A)P(B)<\/code><\/p>\n<p>\u5b9a\u4e49\uff1a\u8bbeA\u3001B\u4e24\u4e8b\u4ef6\u6ee1\u8db3\u7b49\u5f0f <code class=\"katex-inline\">P(AB)=P(A)P(B)<\/code>\uff0c\u5219\u79f0\u4e8b\u4ef6 A \u4e0e\u4e8b\u4ef6 B \u76f8\u4e92\u72ec\u7acb\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E4%BE%8B%E4%B8%80-3\"><\/span>\u4f8b\u4e00<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u7532\u3001\u4e59\u4e24\u4eba\u5c04\u51fb\u540c\u4e00\u76ee\u6807\uff0c\u7532\u5c04\u4e2d\u7684\u6982\u7387\u4e3a 0.8\uff0c\u4e59\u5c04\u4e2d\u7684\u6982\u7387\u4e3a 0.7\uff0c\u6c42\u76ee\u6807\u88ab\u5c04\u4e2d\u7684\u6982\u7387\u3002<\/p>\n<p>\u8bbe A={\u7532\u5c04\u4e2d}\uff0cB={\u4e59\u5c04\u4e2d}\uff0cC={\u76ee\u6807\u88ab\u5c04\u4e2d}<br \/>\nP(A)=0.8\uff0cp(B)=0.7\uff0c<code class=\"katex-inline\">C=A\\cup B<\/code>\uff0cP(C)=P(A)+P(B)-P(AB)<br \/>\nA\u3001B \u76f8\u4e92\u72ec\u7acb\u6709 P(AB)=P(A)P(B)=0.56<br \/>\nP(C)=0.8+0.7-0.56=0.94<\/p>\n<h2><span class=\"ez-toc-section\" id=\"22_%E7%8B%AC%E7%AB%8B%E8%AF%95%E9%AA%8C\"><\/span>2.2 \u72ec\u7acb\u8bd5\u9a8c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u91cd\u590d\u72ec\u7acb\u8bd5\u9a8c\u662f\u6307\u5728\u76f8\u540c\u7684\u6761\u4ef6\u4e0b\u5c06\u8bd5\u9a8c E \u91cd\u590d\u8fdb\u884c\uff0c\u4e14\u6bcf\u6b21\u8bd5\u9a8c\u662f\u72ec\u7acb\u8fdb\u884c\u7684\uff0c\u5373\u6bcf\u6b21\u8bd5\u9a8c\u7ed3\u679c\u51fa\u73b0\u7684\u6982\u7387\u4e0d\u53d7\u5176\u5b83\u5404\u6b21\u8bd5\u9a8c\u7ed3\u679c\u7684\u5f71\u54cd\u3002<br \/>\n\u5982\u679c\u4e00\u4e2a\u968f\u673a\u8bd5\u9a8c E \u53ea\u4ea7\u751f\u4e24\u4e2a\u7ed3\u679c A \u548c <code class=\"katex-inline\">\\overline{A}<\/code>\uff0c\u5219\u79f0 E \u4e3a\u4f2f\u52aa\u5229\u8bd5\u9a8c\uff0c\u5c06 E \u91cd\u590d\u8fdb\u884c n \u6b21\uff0c\u79f0\u4e3a n \u91cd\u4f2f\u52aa\u5229\u8bd5\u9a8c\uff0c\u4e5f\u79f0\u4e3a\u4f2f\u52aa\u5229\u6982\u578b\u3002<\/p>\n<p>\u5b9a\u4e49\uff1an \u91cd\u4f2f\u52aa\u5229\u8bd5\u9a8c\u4e2d\uff0c\u5982\u679c\u6bcf\u6b21\u8bd5\u9a8c\u4e2d\u4e8b\u4ef6 A \u53d1\u751f\u7684\u6982\u7387\u4e3a P(A)=p\uff0c0&lt;p&lt;1\uff0c\u5219\u5728 n \u91cd\u4f2f\u52aa\u5229\u8bd5\u9a8c\u4e2d\u4e8b\u4ef6 A \u6070\u597d\u53d1\u751f k \u6b21\u7684\u6982\u7387\u4e3a <code class=\"katex-inline\">P_n(k)=C_n^kp^k(1-q)^{n-k}<\/code>\uff0ck=1,2,<code class=\"katex-inline\">\\cdots<\/code>,n\u3002<\/p>\n<h3><span class=\"ez-toc-section\" id=\"%E4%BE%8B%E4%B8%80-4\"><\/span>\u4f8b\u4e00<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u629b\u786c\u5e01\u8bd5\u9a8c\u4e2d\uff0c\u6c42\u629b\u51fa 49 \u4e2a\u6b63\u9762\uff0c31 \u4e2a\u53cd\u9762\u7684\u6982\u7387\u3002<\/p>\n<p>\u76f8\u5f53\u4e8e\u8fdb\u884c 80 \u91cd\u4f2f\u52aa\u5229\u8bd5\u9a8c\uff0cX \u8bb0\u4e3a\u629b\u51fa\u6b63\u9762\u7684\u6b21\u6570\uff0c\u6709<br \/>\n<code class=\"katex-inline\">P\\{X=49\\}=C_{80}^{49}0.5^{49}0.5^{31}\\approx0.011836<\/code><\/p>\n<p>\u6ce8\uff1a\u6392\u5217\u7ec4\u5408\u8ba1\u7b97\u53c2\u8003\uff1a<a href=\"https:\/\/blog.iyatt.com\/?p=10812\">https:\/\/blog.iyatt.com\/?p=10812<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>1 \u968f\u673a\u4e8b\u4ef6 \u968f\u673a\u4e8b\u4ef6\u6ee1\u8db3\u7684\u7279\u5f81\uff1a \u53ef\u4ee5\u5728\u60f3\u7528\u6761\u4ef6\u4e0b\u91cd\u590d\u6267\u884c \u4e8b\u5148\u53ef\u77e5\u53ef\u80fd\u51fa\u73b0\u7684\u7ed3\u679c \u8bd5\u9a8c\u5f00\u59cb\u524d\u4e0d\u786e\u5b9a\u5f53\u6b21\u7684\u7ed3 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"zakra_page_container_layout":"customizer","zakra_page_sidebar_layout":"customizer","zakra_remove_content_margin":false,"zakra_sidebar":"customizer","zakra_transparent_header":"customizer","zakra_logo":0,"zakra_main_header_style":"default","zakra_menu_item_color":"","zakra_menu_item_hover_color":"","zakra_menu_item_active_color":"","zakra_menu_active_style":"","zakra_page_header":true,"_lmt_disableupdate":"no","_lmt_disable":"no","footnotes":""},"categories":[1,612],"tags":[],"class_list":["post-14350","post","type-post","status-publish","format-standard","hentry","category-all","category-612"],"modified_by":"IYATT-yx","_links":{"self":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/14350","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=14350"}],"version-history":[{"count":1,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/14350\/revisions"}],"predecessor-version":[{"id":21496,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/14350\/revisions\/21496"}],"wp:attachment":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14350"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14350"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14350"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}