{"id":47158,"date":"2013-10-25T09:00:59","date_gmt":"2013-10-25T01:00:59","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=47158"},"modified":"2021-10-06T16:19:45","modified_gmt":"2021-10-06T08:19:45","slug":"%e8%92%99%e6%8f%90%e9%9c%8d%e7%88%be%e5%95%8f%e9%a1%8c%ef%bc%88monty-hall-problem%ef%bc%89%e4%b8%80-%e6%b1%ba%e5%8b%9d21%e9%bb%9e","status":"publish","type":"post","link":"http:\/\/localhost\/%e8%92%99%e6%8f%90%e9%9c%8d%e7%88%be%e5%95%8f%e9%a1%8c%ef%bc%88monty-hall-problem%ef%bc%89%e4%b8%80-%e6%b1%ba%e5%8b%9d21%e9%bb%9e\/","title":{"rendered":"\u8499\u63d0\u970d\u723e\u554f\u984c\uff08\u4e00\uff09\u6c7a\u52dd21\u9ede"},"content":{"rendered":"

\u8499\u63d0\u970d\u723e\u554f\u984c (Monty Hall problem)\uff08\u4e00\uff09 \u6c7a\u52dd21\u9ede<\/span>
\n\u570b\u7acb\u5c4f\u6771\u9ad8\u7d1a\u4e2d\u5b78\u6578\u5b78\u79d1\u694a\u74ca\u8339\u8001\u5e2b<\/span><\/strong><\/strong><\/p>\n

\u5728 2008 \u5e74\u4e0a\u6620\u7684\u7f8e\u570b\u96fb\u5f71\u300a\u6c7a\u52dd21\u9ede\u300b\u4e2d\uff0c\u5287\u4e2d\u4e3b\u89d2\u73ed (Ben Campbell)\u5728\u975e\u7dda\u6027\u4ee3\u6578\u7684\u8ab2\u5802\u4e0a\u8207\u6388\u8ab2\u6559\u6388\u7c73\u5947(Mickey Rosa) \u6709\u4e00\u6bb5\u7cbe\u5f69\u7684\u5c0d\u8a71\uff1a<\/p>\n

\u7c73\u5947\uff1a\u300c\u5047\u8a2d\u4f60\u6b63\u53c3\u52a0\u4e00\u500b\u904a\u6232\u7bc0\u76ee\uff0c\u4f60\u6709\u6a5f\u6703\u5f9e\u4e09\u6247\u4e0d\u540c\u7684\u9580\u88e1\u9078\u4e00\u6247\uff0c\u5176\u4e2d\u4e00\u6247\u9580\u5f8c\u9762\u6709\u4e00\u8f1b\u65b0\u8eca\uff0c\u53e6\u5916\u5169\u6247\u9580\u5f8c\u9762\u5404\u6709\u4e00\u982d\u5c71\u7f8a\uff1f\u4f60\u8981\u9078\u64c7\u54ea\u4e00\u6247\u9580\uff1f\u300d<\/strong><\/p>\n

\u73ed\uff1a\u00a0 \u300c\u4e00\u865f\u9580\u3002\u300d<\/strong><\/p>\n

\u7c73\u5947\uff1a\u300c\u597d\uff01\u9019\u6642\u7bc0\u76ee\u4e3b\u6301\u4eba\uff0c\u9806\u4fbf\u4e00\u63d0\uff0c\u4ed6\u77e5\u9053\u9580\u5f8c\u7684\u79d8\u5bc6\uff0c\u4ed6\u53bb\u6253\u958b\u53e6\u4e00\u6247\u9580\uff0c\u6bd4\u65b9\u8aaa\u4ed6\u958b\u4e86\u4e09\u865f\u9580\uff0c\u5f8c\u9762\u662f\u4e00\u982d\u5c71\u7f8a\u3002\u9019\u6642\u7bc0\u76ee\u4e3b\u6301\u4eba\u8aaa\uff1a\u300c\u73ed\uff0c\u4f60\u60f3\u8981\u5805\u6301\u9078\u64c7\u4e00\u865f\u9580\uff0c\u9084\u662f\u63db\u6210\u4e8c\u865f\u9580\uff1f\u300d\u73fe\u5728\u554f\u984c\u662f\u2013\u6539\u8b8a\u9078\u64c7(\u63db\u53e6\u4e00\u6247\u9580)\u662f\u5426\u5c0d\u4f60\u6709\u5229?\u300d<\/strong><\/p>\n

\u73ed\uff1a\u00a0 \u300c\u662f\u7684\u300d<\/strong><\/p>\n

\u7c73\u5947\uff1a\u300c\u8a18\u4f4f\uff01\u4e3b\u6301\u4eba\u77e5\u9053\u90a3\u8f1b\u8eca\u5728\u54ea\u88e1\uff0c\u4f60\u600e\u9ebc\u77e5\u9053\u4ed6\u4e0d\u662f\u5728\u800d\u4f60\uff1f\u2026\u2026\u300d<\/strong><\/p>\n

\u73ed\uff1a\u00a0 \u300c\u6211\u4e26\u4e0d\u4ecb\u610f\uff0c\u56e0\u70ba\u6211\u7684\u7b54\u6848\u662f\u57fa\u65bc\u7d71\u8a08\u5b78\uff0c\u2026\u2026\uff0c\u7576\u4e00\u958b\u59cb\u4ed6\u8b93\u6211\u9078\u4e00\u6247\u9580\u6642\uff0c\u6211\u6709 \\(33.3\\%\\) \u7684\u6a5f\u7387\u662f\u9078\u5c0d\u7684\uff0c\u4f46\u7576\u4ed6\u958b\u5176\u4e2d\u4e00\u6247\u9580\u6642\uff0c\u7136\u5f8c\u53c8\u8b93\u6211\u9078\u6642\uff0c\u6b64\u523b\u5982\u679c\u6211\u9078\u64c7\u63db\u4e00\u6247\u9580\uff0c\u9078\u5c0d\u7684\u6a5f\u7387\u662f \\(66.7\\%\\)\uff0c\u2026\u2026\u3002\u300d<\/strong><\/p>\n

\u4e0a\u8ff0\u7684\u5167\u5bb9\u4e2d\u6709\u4e8c\u9805\u689d\u4ef6\u5fc5\u9808\u6ce8\u610f\uff0c\u53c3\u8cfd\u8005\u4e09\u6247\u9580\u4e2d\u9078\u4e00\u6247\u9580\uff0c\u4f46\u4ed6\u4e0d\u77e5\u9053\u9580\u5f8c\u9762\u662f\u65b0\u8eca\u9084\u662f\u5c71\u7f8a\uff0c\u53ef\u662f\u4e3b\u6301\u4eba\u77e5\u9053\u3002\u518d\u8005\uff0c\u4e3b\u6301\u4eba\u958b\u555f\u5269\u4e0b\u5169\u6247\u9580\u4e2d\u7684\u5176\u4e2d\u4e00\u6247\u9580\uff0c\u4e00\u5b9a\u6311\u6709\u5c71\u7f8a\u7684\u9580\uff0c\u4e26\u4e14\u63d0\u4f9b\u53c3\u8cfd\u8005\u63db\u9580\u7684\u6a5f\u6703\u3002<\/p>\n

\u9019\u500b\u984c\u76ee\u7a31\u70ba\u300c\u8499\u63d0\u970d\u723e\u554f\u984c\u300d( Monty Hall problem)\uff0c\u5176\u540d\u7a31\u6e90\u81ea\u7f8e\u570b\u76ca\u667a\u96fb\u8996\u7bc0\u76ee\u300c\u6211\u5011\u6210\u4ea4\u5427\u300d( Let\u2019s Make a Deal )\u4e2d\u7684\u4e3b\u6301\u4eba\u8499\u63d0\u2027\u970d\u723e( Monty Hall )\uff0c\u800c\u4e09\u9580\u554f\u984c\u6b63\u662f\u7bc0\u76ee\u4e2d\u7684\u4e00\u500b\u904a\u6232\u3002<\/p>\n

\u7576\u4e09\u9580\u53ea\u5269\u4e0b\u5169\u9053\u9580\uff0c\u9078\u9805\u8b8a\u6210\u4e8c\u9078\u4e00\u6642\uff0c\u6709\u7684\u53c3\u8cfd\u8005\u76f4\u89ba\u4e0a\u8a8d\u70ba\u65b0\u8eca\u5728\u5169\u9053\u9580\u5f8c\u7684\u6a5f\u6703\u5747\u7b49\uff0c\u8d0f\u5f97\u65b0\u8eca\u7684\u6a5f\u7387\u662f\uff0c\u4e0d\u8ad6\u63db\u6216\u4e0d\u63db\u90fd\u6c92\u6709\u5dee\uff0c\u6240\u4ee5\u5805\u6301\u539f\u4f86\u7684\u9078\u64c7\uff0c\u6253\u6b7b\u4e0d\u63db\u3002<\/p>\n

\u7a76\u7adf\u63db\u6bd4\u8f03\u6709\u5229\uff1f\u9084\u662f\u63db\u4e0d\u63db\u90fd\u6c92\u5dee\uff1f\u6211\u5011\u904b\u7528\u6a39\u72c0\u5716\u5206\u6790\uff1a<\/p>\n

\"47158_p1\"<\/a><\/p>\n

\u7531\u8c9d\u6c0f\u5b9a\u7406\u5f97\u77e5\uff1a<\/p>\n

\u5982\u679c\u5728\u4e0d\u63db\u9580\u7684\u60c5\u5f62\u4e0b\uff0c\u8d0f\u5f97\u65b0\u8eca\u7684\u6a5f\u7387\u662f \\(\\displaystyle \\frac{1\/6}{1\/6+1\/3}=\\frac{1}{3}\\approx 33.3\\%\\)\uff1b<\/p>\n

\u5982\u679c\u5728\u63db\u9580\u7684\u60c5\u5f62\u4e0b\uff0c\u8d0f\u5f97\u65b0\u8eca\u7684\u6a5f\u7387\u662f\u00a0\\(\\displaystyle \\frac{1\/3}{1\/6+1\/3}=\\frac{2}{3}\\approx 66.7\\%\\)\u3002<\/p>\n

\u73ed\u7684\u7b54\u6848\u5b8c\u5168\u6b63\u78ba\uff0c\u4f46\u662f\u76f4\u89ba\u4e0a\u6a5f\u7387 \\(1\/2\\) \u662f\u600e\u9ebc\u56de\u4e8b\uff1f<\/p>\n

\"47158_eq1\"<\/a><\/p>\n

\\(\\displaystyle = \\frac{1}{3}\\times\\frac{1}{2}+\\frac{2}{3}\\times\\frac{1}{2}=\\frac{1}{6}+\\frac{1}{3}=\\frac{1}{2}\\)<\/p>\n

\u6211\u5011\u4e0d\u53ef\u5ffd\u7565\u7684\u662f\uff0c\u7576\u4e3b\u6301\u4eba\u63d0\u4f9b\u8cc7\u8a0a\u4e26\u7d66\u4e88\u63db\u9580\u7684\u6a5f\u6703\u6642\uff0c<\/p>\n

\u65b0\u8eca\u5728\u5269\u4e0b\u5169\u9053\u9580\u5f8c\u7684\u6a5f\u7387\u5176\u5be6\u662f\u4e0d\u76f8\u540c\u7684\uff0c\u5206\u5225\u70ba \\(1\/3\\) \u548c \\(2\/3\\)\uff0c<\/p>\n

\u5373 \\(P(\\) \u8d0f\u5f97\u65b0\u8eca|\u9078\u64c7\u4e0d\u63db \\()=\\displaystyle\\frac{1}{3}\\)\u3001\\(P(\\) \u8d0f\u5f97\u65b0\u8eca|\u9078\u64c7\u63db\u9580 \\()=\\displaystyle\\frac{2}{3}\\)\uff0c<\/p>\n

\u8981\u63db\u624d\u6709\u512a\u52e2\uff01<\/p>\n

\u900f\u904e\u4e0a\u8ff0\u8a0e\u8ad6\uff0c\u63db\u9580\u78ba\u5be6\u662f\u660e\u667a\u7684\u9078\u64c7\uff0c\u4f46\u662f\u6a5f\u7387\u503c\u4e5f\u986f\u793a\uff0c\u4e0d\u4fdd\u8b49\u63db\u9580\u4e00\u5b9a\u8d0f\uff01\u7562\u7adf\uff0c\u5728\u9084\u6c92\u958b\u51fa\u7d50\u679c\u4e4b\u524d\uff0c\u6240\u6709\u7684\u53ef\u80fd\u90fd\u662f\u53ef\u80fd\u3002<\/p>\n

\u9023\u7d50\uff1a\u8499\u63d0\u970d\u723e\u554f\u984c\uff08\u4e8c\uff09\u8acb\u554f\u746a\u9e97\u84ee<\/a><\/p>\n

\n

\u53c3\u8003\u8cc7\u6599<\/strong><\/p>\n

    \n
  1. \u66fc\u7f85\u8fea\u8afe\u8457\u3001\u80e1\u5b88\u4ec1\u8b6f(2012)\uff0c\u300a\u9189\u6f22\u8d70\u8def\u2013\u6a5f\u7387\u5982\u4f55\u5de6\u53f3\u4f60\u6211\u7684\u547d\u904b\u548c\u6a5f\u6703\u300b\uff0c\u53f0\u5317\uff1a\u5929\u4e0b\u9060\u898b\u51fa\u7248\u793e\u3002<\/li>\n
  2. \u300a\u6c7a\u52dd21\u9ede\u300b(2008)\uff0c\u54e5\u502b\u6bd4\u4e9e\u5f71\u696d\u88fd\u4f5c\u3002<\/li>\n<\/ol>\n<\/div>","protected":false},"excerpt":{"rendered":"

    \u8499\u63d0\u970d\u723e\u554f\u984c (Monty Hall problem)\uff08\u4e00\uff09 \u6c7a\u52dd21\u9ede \u570b\u7acb\u5c4f\u6771\u9ad8\u7d1a\u4e2d\u5b78\u6578\u5b78\u79d1\u694a\u74ca\u8339\u8001\u5e2b \u5728…<\/p>\n","protected":false},"author":50,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[111,229],"tags":[8120,5676,2384,5675,4846],"class_list":["post-47158","post","type-post","status-publish","format-standard","hentry","category-mathematics00","category-math06","tag-monty-hall","tag-5676","tag-2384","tag-5675","tag-4846","loop-entry","cat-111","cat-229","no-thumbnail"],"views":57686,"_links":{"self":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/47158","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/users\/50"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/comments?post=47158"}],"version-history":[{"count":1,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/47158\/revisions"}],"predecessor-version":[{"id":87348,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/posts\/47158\/revisions\/87348"}],"wp:attachment":[{"href":"http:\/\/localhost\/wp-json\/wp\/v2\/media?parent=47158"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/categories?post=47158"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/localhost\/wp-json\/wp\/v2\/tags?post=47158"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}