{"id":39287,"date":"2011-09-05T20:39:30","date_gmt":"2011-09-05T12:39:30","guid":{"rendered":"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/?p=39287"},"modified":"2021-10-06T16:23:03","modified_gmt":"2021-10-06T08:23:03","slug":"%e6%a9%9f%e7%8e%87%e6%ad%b7%e5%8f%b2the-history-of-probability","status":"publish","type":"post","link":"http:\/\/localhost\/%e6%a9%9f%e7%8e%87%e6%ad%b7%e5%8f%b2the-history-of-probability\/","title":{"rendered":"\u6a5f\u7387\u6b77\u53f2"},"content":{"rendered":"<div class=\"pf-content\"><p><strong><span style=\"color: #ff6600;\">\u6a5f\u7387\u6b77\u53f2 (The History of Probability)<\/span><br \/>\n<span style=\"color: #008000;\">\u570b\u7acb\u862d\u967d\u5973\u4e2d\u6578\u5b78\u79d1\u9673\u654f\u6667\u8001\u5e2b\/\u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u6578\u5b78\u7cfb\u8a31\u5fd7\u8fb2\u6559\u6388\u8cac\u4efb\u7de8\u8f2f <\/span><\/strong><\/p>\n<p><strong>\u81ea\u53e4\u4ee5\u4f86\uff0c\u5c0d\u65bc\u4e0d\u53ef\u9810\u77e5\u7684\u4e8b\u60c5\uff0c\u4eba\u5011\u7e3d\u662f\u5145\u6eff\u8457\u597d\u5947\uff0c\u4e26\u4e14\u5728\u597d\u5947\u5fc3\u7684\u9a45\u4f7f\u4e0b\uff0c\u5f80\u5f80\u7522\u751f\u4e86\u4e00\u4e9b\u6216\u5c0d\u6216\u932f\u7684\u6cd5\u5247\u3002\u59d1\u4e14\u4e0d\u8ad6\u5176\u52d5\u6a5f\u70ba\u4f55\uff0c\u9019\u4e9b\u6cd5\u5247\u537b\u53ef\u80fd\u56e0\u6b64\u958b\u5275\u53e6\u4e00\u9818\u57df\u6216\u5b78\u79d1\uff0c\u6a5f\u7387\u8ad6\uff08theory of probability\uff09\u7684\u767c\u5c55\u4fbf\u662f\u5982\u6b64\u3002<\/strong><\/p>\n<p>\u897f\u65b9\u5b78\u8005\u65bc 17 \u4e16\u7d00\u958b\u59cb\u5c0d\u6a5f\u7387\u7406\u8ad6\u7522\u751f\u8208\u8da3\uff0c\u5176\u7406\u8ad6\u80cc\u666f\u6700\u521d\u53ea\u662f\u70ba\u4e86\u8655\u7406\u5982\u64f2\u9ab0\u5b50\u3001\u8f2a\u76e4\u3001\u64b2\u514b\u724c\u7b49\u904a\u6232\u7684\u8ced\u91d1\u5206\u914d\u554f\u984c\u3002\u5176\u4e2d\u64f2\u9ab0\u5b50\u65e9\u671f\u6d41\u884c\u65bc\u57c3\u53ca\u3001\u5370\u5ea6\u53ca\u6771\u65b9\u6c11\u65cf\uff0c\u5e0c\u81d8\u4eba\u628a\u64f2\u9ab0\u5b50\u904a\u6232\u7684\u767c\u660e\uff0c\u6b78\u529f\u65bc\u7279\u6d1b\u4f0a\u57ce\u88ab\u570d\u56f0\u6642\u7684\u5e15\u62c9\u58a8\u5f97\u65af\uff0c\u7576\u6642\u7684\u4eba\u5011\u90fd\u5341\u5206\u71b1\u8877\u6b64\u904a\u6232\u3002\u53e4\u7f85\u99ac\u4eba\u4e5f\u4e0d\u5e72\u793a\u5f31\uff0c\u514b\u52de\u72c4\u7687\u5e1d\u9084\u89aa\u81ea\u64b0\u5beb\u6709\u95dc\u64f2\u9ab0\u5b50\u7684\u6587\u7ae0\u3002\u800c\u5728\u300a\u6469\u8efb\u5a46\u7f85\u591a\u300b\u9019\u90e8\u6709 3000 \u5e74\u7684\u5370\u5ea6\u6558\u4e8b\u8a69\u4e2d\uff0c\u7d00\u9304\u4e86\u4e00\u4f4d\u72c2\u71b1\u7684\u64f2\u9ab0\u5b50\u8ced\u5f92\u7684\u4e0d\u5e78\uff0c\u4ed6\u5728\u8f38\u5149\u4e86\u4e00\u5207\u4e4b\u5f8c\uff0c\u7adf\u7136\u62ff\u81ea\u5df1\u7684\u751f\u547d\u505a\u8ced\u6ce8\uff0c\u771f\u662f\u4ee4\u4eba\u60cb\u60dc\u7684\u4e00\u6bb5\u6b77\u53f2\u3002<!--more--><\/p>\n<p><a href=\"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/wp-content\/uploads\/2011\/09\/Wuerfel5.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-52635\" src=\"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/wp-content\/uploads\/2011\/09\/Wuerfel5.jpg\" alt=\"Wuerfel5\" width=\"400\" height=\"300\" srcset=\"http:\/\/localhost\/wp-content\/uploads\/2011\/09\/Wuerfel5.jpg 640w, http:\/\/localhost\/wp-content\/uploads\/2011\/09\/Wuerfel5-300x225.jpg 300w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a><\/p>\n<p>\u95dc\u65bc\u6a5f\u7387\uff0c\u4e00\u4e9b\u6559\u79d1\u66f8\u901a\u5e38\u90fd\u4ee5\u6cd5\u570b\u8cb4\u65cf\u9ed8\u52d2(Chevalier de Mere)\u8acb\u6559\u5df4\u65af\u5361(Blaise Pascal, 1601-1665)\u9ab0\u5b50\u64f2\u9ede\u554f\u984c\u4f5c\u70ba\u51fa\u767c\u9ede\u3002\u554f\u984c\u70ba\uff1a\u300c\u64f2\u4e00\u500b\u9ab0\u5b50\u56db\u6b21\u81f3\u5c11\u6709\u4e00\u6b21\u51fa\u73fe\u9ede\u6578 \\(1\\) \u7684\u6a5f\u6703\uff0c\u8207\u64f2\u4e00\u5c0d\u9ab0\u5b50 \\(24\\) \u6b21\u81f3\u5c11\u6709\u96d9 \\(1\\)(\u5169\u500b\u9ab0\u5b50\u90fd\u51fa\u73fe\u9ede\u6578 \\(1\\))\u7684\u6a5f\u6703\uff0c\u4f55\u8005\u8f03\u5927\uff1f\u300d<\/p>\n<p>\u9ed8\u52d2\u8a8d\u70ba\u662f\u76f8\u540c\uff0c\u7406\u7531\u5982\u4e0b\uff1a\u7b2c\u4e00\u7a2e\u64f2\u6cd5\uff1a\u6bcf\u64f2\u4e00\u6b21\u9ab0\u5b50\uff0c\u6709 \\(1\/6\\) \u7684\u6a5f\u6703\u51fa\u73fe\u9ede\u6578 \\(1\\)\uff0c\u56e0\u6b64\uff0c\u64f2\u56db\u6b21\u9ab0\u5b50\uff0c\u6709 \\(4\\times 1\/6=2\/3\\) \u00a0\u7684\u6a5f\u6703\u51fa\u73fe\u9ede\u6578 \\(1\\)\u3002\u7b2c\u4e8c\u7a2e\u64f2\u6cd5\uff1a\u6bcf\u64f2\u4e00\u5c0d\u9ab0\u5b50\uff0c\u6709 \\(1\/36\\) \u7684\u6a5f\u6703\u51fa\u73fe\u5169\u500b\u9ab0\u5b50\u9ede\u6578\u5747\u70ba \\(1\\)\uff0c\u56e0\u6b64\uff0c\u64f2 \\(24\\) \u6b21\u9ab0\u5b50\uff0c\u6709 \\(24\\times 1\/36=2\/3\\) \u7684\u6a5f\u6703\u51fa\u73fe\u5169\u500b\u9ab0\u5b50\u9ede\u6578\u5747\u70ba \\(1\\)\u3002\u9ed8\u52d2\u7684\u60f3\u6cd5\u5f88\u660e\u986f\u662f\u932f\u8aa4\u7684\uff0c\u4ed6\u8a8d\u70ba\u6bcf\u64f2 \\(6\\) \u6b21\u9ab0\u5b50\u300c\u5fc5\u7136\u300d\u6709\u4e00\u6b21\u51fa\u73fe\u4e00\u9ede\uff0c\u6240\u4ee5\uff0c\u624d\u5c0e\u81f4\u932f\u8aa4(\u9019\u4e5f\u662f\u4e00\u822c\u5b78\u751f\u5e38\u72af\u7684\u932f\u8aa4\u985e\u578b)\u3002<\/p>\n<p>\u5f9e\u9019\u88e1\u6211\u5011\u53ef\u4ee5\u770b\u5230\uff0c\u6a5f\u7387\u8ad6\u767c\u5c55\u4e4b\u521d\u4e26\u4e0d\u662f\u4e00\u5e06\u98a8\u9806\u7684\uff0c\u800c\u662f\u5148\u6709\u4e86\u4e00\u4e9b\u8cea\u6a38\u4f46\u4e0d\u4e00\u5b9a\u6b63\u78ba\u7684\u60f3\u50cf\u3002\u73fe\u884c\u6559\u79d1\u66f8\u4e2d\u7684\u7de8\u6392\u65b9\u5f0f\uff0c\u6703\u8b93\u8a31\u591a\u5b78\u751f\u8aa4\u8a8d\u70ba\u6240\u6709\u7684\u6578\u5b78\u77e5\u8b58\uff0c\u7686\u6191\u85c9\u8457\u4e00\u4e9b\u8070\u7a4e\u7684\u60f3\u6cd5(idea)\u800c\u975e\u4e00\u4e9b\u6210\u529f\u6216\u5931\u6557\u7684\u7d2f\u7a4d\u904e\u7a0b\u3002\u6240\u4ee5\uff0c\u6211\u5011\u61c9\u9084\u539f\u6b77\u53f2\u7684\u59cb\u672b\uff0c\u7d66\u4e88\u5b78\u751f\u66f4\u591a\u7684\u6d1e\u5bdf\u529b(insight)\u53ca\u60f3\u50cf\u529b(imagination)\u3002(\u8a3b 1)<\/p>\n<p>\u63a5\u4e0b\u4f86\uff0c\u518d\u4ecb\u7d39\u9ed8\u52d2\u7684\u53e6\u4e00\u500b\u554f\u984c\uff1a\u300c\u5169\u4eba\u6bd4\u8cfd\u5404\u51fa\u8cc7\u8ced\u91d1 \\(32\\) \u91d1\u5e63\uff0c\u898f\u5b9a\u5fc5\u9808\u8981\u8d0f\u4e09\u5c40\u624d\u80fd\u8d0f\u5f97\u8ced\u91d1(stakes)\uff0c\u4f46\u5f8c\u4f86\u6bd4\u8cfd\u56e0\u6545\u7d42\u6b62\uff0c\u4e14\u52dd\u5c40\u6bd4\u70ba \\((1,0)\\)\uff0c\u554f\u6b64\u6642\u5982\u4f55\u5206\u8ced\u91d1\uff1f\u300d\u6b64\u5916\uff0c\u5e15\u5947\u6b50\u91cc(Luca Pacioli, 1446-1517)\u8457\u6709\u7b2c\u4e00\u672c\u6578\u5b78\u53f2\u4e0a\u5305\u62ec\u6a5f\u7387\u554f\u984c\u7684\u66f8\u7c4d\uff0c\u672c\u66f8\u65bc 1494\u5e74\u5728\u7fa9\u5927\u5229\u5a01\u5c3c\u65af\u51fa\u7248\uff0c\u66f8\u4e2d\u6709\u4e00\u984c\u5982\u4e0b\uff1a\u300c\u5169\u4eba\u6bd4\u8cfd\u5404\u51fa\u8cc7\u8ced\u91d1 \\(32\\) \u91d1\u5e63\uff0c\u898f\u5b9a\u5fc5\u9808\u8d0f\u4e09\u5c40\u624d\u80fd\u8d0f\u5f97\u8ced\u91d1\uff0c\u4f46\u5f8c\u4f86\u6bd4\u8cfd\u56e0\u6545\u7d42\u6b62\uff0c\u4e14\u52dd\u5c40\u6bd4\u70ba \\((2,0)\\)\uff0c\u554f\u6b64\u6642\u5982\u4f55\u5206\u8ced\u91d1\uff1f\u300d<\/p>\n<div>\n<p>\u9019\u5e7e\u500b\u554f\u984c\uff0c\u5f15\u767c\u6578\u5b78\u5bb6\u5361\u7576\u8afe(Girolamo Cardano, 1501-1576)\u53ca\u5854\u723e\u5854\u5229\u4e9e(Niccolo Tartaglia, 1499-1557)\u7684\u8208\u8da3\uff0c\u4f46\u76f4\u5230\u5361\u7576\u8afe\u6b7b\u5f8c\u5176\u89e3\u6cd5\u624d\u51fa\u73fe\u3002\u540c\u6642\uff0c\u773e\u6240\u7686\u77e5\u7684\u5049\u5927\u79d1\u5b78\u5bb6\u4f3d\u5229\u7565(Galileo Galilei, 1564-1642)\u4e5f\u66fe\u5beb\u904e\u6709\u95dc\u6a5f\u7387\u7684\u66f8\u7c4d\uff0c\u53ef\u60dc\uff0c\u4e26\u672a\u6d41\u50b3\u4e0b\u4f86\u3002\u76f4\u5230 1654\u5e74\u590f\u5929\uff0c\u9019\u4e9b\u554f\u984c\u88ab 17\u4e16\u7d00\u6cd5\u570b\u6700\u5049\u5927\u7684\u6578\u5b78\u5bb6\u5df4\u65af\u5361\u8207\u8cbb\u746a(Pierre de Fermat, 1601-1665)\u5229\u7528\u66f8\u4fe1\u7684\u5f80\u8fd4\u8a0e\u8ad6\u624d\u89e3\u6c7a\uff0c\u624d\u5960\u7acb\u4e86\u6a5f\u7387\u8ad6\u7684\u57fa\u790e\u3002<\/p>\n<\/div>\n<p><span style=\"color: #000080;\"><strong>\u6a5f\u7387\u8ad6\u7684\u5efa\u7acb<\/strong>\u00a0<\/span><\/p>\n<p>\u83ab\u52d2\u8acb\u6559\u5df4\u65af\u5361\u9ab0\u5b50\u64f2\u9ede\u554f\u984c\u662f\u5efa\u7acb\u6a5f\u7387\u7406\u8ad6\u7684\u89f8\u5a92\uff0c\u63a5\u4e0b\u4f86\u5df4\u65af\u5361\u5247\u5beb\u4fe1\u8acb\u6559\u8cbb\u746a(\u53ef\u60dc\u4fe1\u5df2\u907a\u5931\u4e86)\uff0c\u8cbb\u746a\u7dca\u63a5\u65bc 1654 \u5e74 7\u6708 27\u65e5\u661f\u671f\u4e00\u56de\u4fe1\uff0c\u63d0\u51fa\u4e86\u89e3\u6cd5\u3002\u5169\u5929\u5f8c\u5df4\u65af\u5361\u56de\u5fa9\uff1a\u300c\u9019\u500b\u65b9\u6cd5\u662f\u975e\u5e38\u53ef\u4fe1\u8cf4\u7684(reliable)\u4e26\u4e14\u662f\u6211\u7b2c\u4e00\u6b21\u898b\u904e\u7684\u3002\u300d\u5df4\u65af\u5361\u5ba3\u7a31\u767c\u73fe\u4e86\u66f4\u77ed\u4e14\u66f4\u7c21\u55ae(much shorter and simpler)\u7684\u4e0d\u540c\u65b9\u6cd5\uff0c\u6700\u5f8c\uff0c\u4ed6\u5728\u4fe1\u7d50\u5c3e\u8655\u66f4\u8868\u73fe\u4e86\u611f\u6027\u53ca\u771f\u8aa0\u7684\u60c5\u8abc\uff0c\u8aaa\u9053\uff1a\u300c\u771f\u7406\u7121\u8ad6\u5728\u5df4\u9ece\u6216\u5410\u52d2\u65af\uff08\u6cd5\u570b\u897f\u5357\u90e8\uff09\u7686\u76f8\u540c\u3002(Truth is same of Toulouse and at Paris)\u300d<\/p>\n<p>\u4ee5\u4e0b\uff0c\u8b93\u6211\u5011\u4e00\u540c\u4f86\u6b23\u8cde\u5df4\u65af\u5361\u7684\u5091\u4f5c\u3002\u9996\u5148\uff0c\u898f\u5b9a\u5fc5\u9808\u8981\u8d0f\u4e09\u5c40\u624d\u80fd\u8d0f\u5f97\u8ced\u91d1\uff0c\u5148\u8003\u616e\u5169\u4eba\u52dd\u5c40 \\((2,1)\\)\uff0c\\((2,0)\\)\uff0c\\((1,0)\\)\u3002\u8acb\u6ce8\u610f\uff1a\u6bcf\u4eba\u51fa\u8ced\u91d1 \\(32\\) \u91d1\u5e63\uff0c\u9019\u500b\u6578\u76ee\u662f\u7d93\u904e\u6311\u9078\uff0c\u4ee5\u4fbf\u4f7f\u7b54\u6848\u7522\u751f\u6700\u7c21\u55ae\u7684\u6574\u6578\u6bd4\u3002<\/p>\n<p>\u7b2c\u4e00\u7a2e\u72c0\u6cc1 \\((2,1)\\)\uff0c\u662f\u6bd4\u8f03\u5bb9\u6613\u7406\u89e3\u7684\u3002<\/p>\n<p>\u5982\u679c\u7e7c\u7e8c\u6bd4\u8cfd\uff0c\u7b2c\u4e00\u4f4d\u518d\u8d0f\u4e00\u5c40\u7684\u8a71\uff0c\u4ed6\u5c07\u8d0f\u5f97\u6240\u6709\u7684\u91d1\u5e63\uff0c\u5373 \\(64\\) \u500b\u91d1\u5e63\uff1a\u5982\u679c\u7b2c\u4e8c\u4f4d\u8d0f\u4e00\u5c40\u7684\u8a71\uff0c\u6bd4\u5c40\u5c07\u70ba \\((2,2)\\)\uff0c\u6bcf\u500b\u4eba\u5747\u5206\u6240\u6709\u7684\u91d1\u5e63\uff0c\u5373 \\(32\\) \u500b\u91d1\u5e63\uff0c\u56e0\u6b64\u7d50\u679c\u5206\u6cd5\u70ba \\([64:0]\\)\uff0c\\([32:32]\\)\u3002\u6240\u4ee5\u7b2c\u4e00\u4f4d\u9078\u624b\u78ba\u5b9a\u6709 \\(32\\) \u500b\u91d1\u5e63\uff0c\u800c\u5269\u9918\u7684\u5747\u5206\u5373 \\(16\\)\u3001\\(16\\)\uff0c\u6240\u4ee5\uff0c\u7d42\u6b62\u6bd4\u8cfd\u7684\u6b63\u78ba\u5206\u6cd5\u70ba \\([48:16]\\)\u3002(\u8a3b 2)<\/p>\n<p>\u7b2c\u4e8c\u7a2e\u72c0\u6cc1 \\((2,0)\\)\uff0c\u525b\u597d\u56de\u7b54\u4e86\u5148\u524d\u5e15\u5947\u6b50\u91cc\u6240\u63d0\u51fa\u7684\u554f\u984c\u3002<\/p>\n<p>\u5982\u679c\u7e7c\u7e8c\u6bd4\u8cfd\uff0c\u7b2c\u4e00\u4f4d\u81f3\u5c11\u6709 \\(48\\) \u500b\u91d1\u5e63\uff0c\u5916\u52a0 \\(16\\) \u7684\u4e00\u534a\u5373 \\(8\\)\u3001\\(8\\)\uff0c\u6240\u4ee5\uff0c\u7d42\u6b62\u6bd4\u8cfd\u7684\u6b63\u78ba\u5206\u6cd5\u70ba \\([56:8]\\) \uff0c\u6700\u7c21\u55ae\u6574\u6578\u6bd4\u70ba \\([7:1]\\)\uff0c\u6b64\u70ba\u5e15\u5947\u6b50\u91cc\u554f\u984c\u7684\u7b54\u6848\u3002<\/p>\n<p>\u7b2c\u4e09\u7a2e\u72c0\u6cc1 \\((1,0)\\)\uff0c\u5247\u662f\u56de\u7b54\u9ed8\u52d2\u6240\u63d0\u7684\u554f\u984c\u3002<\/p>\n<p>\u5982\u679c\u7b2c\u4e00\u4f4d\u518d\u8d0f\u4e00\u5c40\u7684\u8a71\uff0c\u6bd4\u6578\u5c07\u70ba \\((2,0)\\)\uff0c\u7b2c\u4e00\u4f4d\u5c07\u53d6\u8d70 \\(56\\) \u500b\u91d1\u5e63\uff0c\u5982\u679c\u7b2c\u4e00\u4f4d\u8f38\u7684\u8a71\u6bd4\u6578\u5c07\u70ba \\((1,1)\\)\uff0c\u7b2c\u4e00\u4f4d\u5c07\u53d6\u8d70 \\(32\\) \u500b\u91d1\u5e63\uff0c\u6240\u4ee5\u7b2c\u4e00\u4f4d\u5c07\u62ff \\(32\\) \u500b\u91d1\u5e63\uff0c\u5916\u52a0(\\(56\\) \u6e1b \\(32\\))\u7684\u4e00\u534a\u5373 \\(12\\)\u3001\\(12\\)\uff0c\u7d42\u6b62\u6bd4\u8cfd\u7684\u6b63\u78ba\u5206\u6cd5\u70ba \\([44:20]\\) \uff0c\u6700\u7c21\u55ae\u7684\u6574\u6578\u6bd4\u70ba \\([11:5]\\) \u3002<\/p>\n<p>\u81f3\u65bc\u8cbb\u746a\u7684\u89e3\u6cd5\uff0c\u5247\u662f\u6839\u64da\u9084\u6709\u5e7e\u5834\u9700\u8981\u6bd4\u8cfd\u624d\u80fd\u770b\u51fa\u8d0f\u5bb6(winner)\u3002\u5982\u679c\u7b2c\u4e00\u4f4d\u9700\u8981\u518d\u6bd4 \\(m\\) \u5834\u624d\u8d0f\uff0c\u800c\u4e14\u7b2c\u4e8c\u4f4d\u9700\u8981\u518d\u6bd4 \u00a0\\(n\\) \u5834\u624d\u8d0f\uff0c\u5247\u9700\u518d\u7d93\u904e \\(m+n-1\\) \u5834\u624d\u80fd\u5ba3\u4f48\u8d0f\u5bb6\u3002\u4f8b\u5982\uff1a\u9ed8\u52d2\u554f\u984c\u4e2d\uff0c\u52dd\u5c40\u6bd4\u70ba \\((1,0)\\)\uff0c\u8cbb\u746a\u63a5\u4e0b\u4f86\u7684\u56db\u5834\u6bd4\u8cfd\u53ef\u80fd\u7d50\u679c\u5217\u51fa\u5982\u4e0b\uff1a(\\(a\\) \u4ee3\u8868\u7b2c\u4e00\u4f4d\u7372\u52dd\uff1b\\(b\\) \u4ee3\u8868\u7b2c\u4e8c\u4f4d\u7372\u52dd)\uff0c\u6700\u5f8c\u7684 \\(1\\)\u3001\\(2\\) \u8868\u793a\u7d50\u679c\u7372\u52dd\u7684\u9078\u624b\u3002<\/p>\n<p style=\"text-align: left;\"><a href=\"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/wp-content\/uploads\/2011\/09\/The-History-of-Probability-1.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-39288\" title=\"The History of Probability-1\" src=\"http:\/\/highscope.ch.ntu.edu.tw\/wordpress\/wp-content\/uploads\/2011\/09\/The-History-of-Probability-1.jpg\" alt=\"\" width=\"357\" height=\"93\" \/><\/a><\/p>\n<p style=\"text-align: left;\">\u6240\u4ee5\uff0c\u8cbb\u746a\u8a8d\u70ba\u5169\u4f4d\u61c9\u8a72\u5206\u7684\u6bd4\u4f8b\u70ba \\([11:5]\\)\uff0c\u9019\u500b\u7d50\u679c\u8ddf\u5df4\u65af\u5361\u6240\u5f97\u5230\u7d50\u679c\u76f8\u540c\u3002\u4f46\u662f\uff0c\u4e00\u4f4d\u5df4\u9ece\u7684\u6578\u5b78\u5bb6\u7f85\u8c9d\u74e6\u723e(Giles de Roberval\uff0c1602-1675)\uff0c\u537b\u6301\u4e0d\u540c\u7684\u770b\u6cd5\uff0c\u4ed6\u8a8d\u70ba\u6709\u4e9b\u6bd4\u8cfd\u4e0d\u9700\u8981\u5217\u51fa\u56db\u5c40\uff0c\u6709\u4e9b\u53ea\u9700\u4e8c\u3001\u4e09\u5c40\u3002\u800c \\((a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4\\)\u00a0\u8cbb\u746a\u7684\u89e3\u6cd5\uff0c\u537b\u626f\u51fa\u4e8c\u9805\u5f0f\u5b9a\u7406\uff1a\\(a\\)\uff0c\\(b\\) \u8996\u70ba\u5169\u9805\uff0c\u56db\u6b21\u5c55\u958b\u5f0f\u4e4b\u4fc2\u6578\u5206\u5225\u70ba \\(1\\)\u3001\\(4\\)\u3001\\(6\\)\u3001\\(4\\)\u3001\\(1\\)(\u8a3b 3)\uff0c\u6240\u4ee5\uff0c\u5206\u6cd5\u70ba \\([1+4+6:4+1]=[11:5]\\)\u3002\u7531\u65bc\u5df4\u65af\u5361\u8207\u8cbb\u746a\u9365\u800c\u4e0d\u6368\u7684\u7cbe\u795e\uff0c\u4f7f\u6a5f\u7387\u7406\u8ad6\u6709\u4e86\u5b8c\u6574\u7684\u5efa\u7acb\uff0c\u4e26\u9020\u5c31\u62c9\u666e\u62c9\u65af\u6210\u70ba\u6a5f\u7387\u8ad6\u7684\u96c6\u5927\u6210\u8005\u3002<\/p>\n<p style=\"text-align: left;\">1655 \u5e74\uff0c\u8377\u862d\u6578\u5b78\u5bb6\u60e0\u66f4\u65af(Christiaan Huygens, 1629-1695)\u8d70\u8a2a\u5df4\u9ece\uff0c\u900f\u904e\u7f85\u8c9d\u74e6\u723e\u7684\u4ecb\u7d39\uff0c\u800c\u5f97\u4ee5\u77ad\u89e3\u5df4\u65af\u5361\u8207\u8cbb\u746a\u4f5c\u54c1\u7684\u5167\u5bb9\uff0c\u4e26\u4e14\u65bc 1657 \u5e74\u5beb\u6709\u95dc\u6a5f\u7387\u65b9\u9762\u7684\u7c21\u77ed\u8ad6\u8457\u300a\u8ad6\u8cfd\u5c40\u904a\u6232\u7684\u8a08\u7b97(On the Calculations in Games of\u00a0Chance)\u300b\uff0c\u66f8\u4e2d\u53ea\u6709\u5341\u56db\u689d\u8ad6\u8ff0(proposition)\uff0c\u800c\u4e14\u7559\u4e0b\u4e94\u500b\u7df4\u7fd2\u984c\u7d66\u8b80\u8005\u6f14\u7df4\u3002\u5f8c\u4f86\uff0c\u96c5\u514b\uff0e\u4f2f\u52aa\u529b(Jacob Bernouli, 1654-1705)\u7528\u9019\u672c\u8ad6\u8457\u4f86\u8a3b\u89e3\u4ed6\u81ea\u5df1\u7684\u300a\u731c\u5ea6\u8853(Ars Conjectandi)\u300b(1713)\uff0c\u5176\u4e2d\u5169\u4f4d\u5be6\u529b\u4e0d\u76f8\u7576\u7684\u9078\u624b\u6bd4\u8cfd\u7684\u76f8\u95dc\u554f\u984c\uff0c\u4e5f\u662f\u7531\u4f2f\u52aa\u529b\u6240\u767c\u5c55\u51fa\u4f86\u7684\u3002<\/p>\n<p style=\"text-align: left;\">\u62c9\u666e\u62c9\u65af(Pierre de Laplace, 1749-1827)\u7684\u300a\u6a5f\u7387\u7684\u5206\u6790\u7406\u8ad6(Analytic Theory\u00a0of Probabilities)\u300b\u5247\u52a0\u5ee3\u4e14\u52a0\u6df1\u6a5f\u7387\u7684\u6578\u5b78\u7406\u8ad6\uff0c\u4e0d\u53ea\u662f\u8ced\u535a\u554f\u984c\u800c\u5df2\u3002\u5728\u4ed6\u4e4b\u524d\uff0c\u6a5f\u7387\u7684\u7406\u8ad6\u53ea\u662f\u7c21\u55ae\u7684\u8cfd\u5c40\u904a\u6232\u800c\u5df2\uff0c\u800c\u62c9\u666e\u62c9\u65af\u5c07\u6a5f\u7387\u7406\u8ad6\u8f49\u5f80\u5176\u4ed6\u6578\u5b78\u5206\u652f(\u4f8b\u5982\uff1a\u932f\u8aa4\u5206\u6790\u8207\u6578\u7406\u7d71\u8a08)\u751a\u81f3\u65bc\u904b\u7528\u5230\u5929\u6587\u5b78\u4e0a\uff1b\u6b64\u5916\uff0c\u4ed6\u5229\u7528\u4eba\u53e3\u7684\u62bd\u6a23\u65b9\u6cd5\u4f86\u4f30\u8a08\u6cd5\u570b\u7684\u4eba\u53e3\u7e3d\u6578\uff0c\u5982\u6b64\u4e00\u4f86\uff0c\u4f7f\u5f97\u6a5f\u7387\u7406\u8ad6\u5728\u6578\u5b78\u4e2d\u4f54\u6709\u4e00\u5e2d\u4e4b\u5730\uff0c\u56e0\u6b64\uff0c\u7d93\u7531\u4ee5\u4e0a\u5e7e\u4f4d\u6578\u5b78\u5bb6\u7684\u52aa\u529b\uff0c\u6a5f\u7387\u8ad6\u6b63\u5f0f\u7372\u5f97\u5efa\u7acb\u3002<\/p>\n<p style=\"text-align: left;\">\u7e3d\u4e4b\uff0c\u300c\u6a5f\u7387\u300d\u662f\u500b\u73fe\u4ee3\u4eba\u5e38\u7528\u7684\u8a9e\u8a00\uff0c\u4f46\u5b83\u7684\u8d77\u6e90\u5c31\u5b9b\u5982\u4e00\u5834\u300c\u7f8e\u9e97\u7684\u76f8\u9047\u300d\uff0c\u82e5\u4e0d\u662f\u5df4\u65af\u5361\u3001\u8cbb\u746a\u5169\u4eba\u5177\u6709\u8ffd\u6839\u7a76\u67e2\u7684\u7cbe\u795e\uff0c\u5c07\u6a5f\u9047\u8cfd\u5c40\u904a\u6232(game of\u00a0chance\uff0c\u5982\u64f2\u9ab0\u5b50\u3001\u8f49\u8f2a\u76e4\u3001\u64b2\u514b\u724c\u7b49)\u767c\u63ee\u5230\u6975\u81f4\uff0c\u9032\u800c\u7814\u7a76\u8a31\u591a\u6709\u95dc\u6a5f\u7387\u7406\u8ad6\uff0c\u6a5f\u7387\u8ad6\u7684\u6b77\u53f2\u5c31\u4e0d\u6703\u5982\u6b64\u591a\u5f69\u591a\u59ff\u3002\u770b\u5b8c\u6b64\u5c0f\u54c1\u4ecb\u7d39\u6a5f\u7387\u53f2\u4e4b\u5f8c\uff0c\u662f\u4e0d\u662f\u8b93\u4f60\u5c0d\u65bc\u6a5f\u7387\u8ad6\u7684\u8d77\u6e90\u6709\u4e86\u8f03\u6df1\u523b\u7684\u4e86\u89e3\u5462\uff1f<\/p>\n<p style=\"text-align: left;\">\u8a3b \\(1:\\) \u9ab0\u5b50\u64f2\u9ede\u554f\u984c\u767c\u5c55\u8207\u5df4\u65af\u5361\u4e09\u89d2\u5f62\u3001\u7d44\u5408\u516c\u5f0f\u3001\u4e8c\u9805\u5f0f\u5b9a\u7406\u5747\u6709\u5bc6\u4e0d\u53ef\u5206\u7684\u95dc\u4fc2\u3002\u9019\u4e9b\u554f\u984c\u4e5f\u51fa\u73fe\u5728\u4f0a\u65af\u862d\u6c11\u65cf\u4e2d\u7684\u907a\u7522\u5206\u914d\u3002\u898b\u8607\u610f\u96ef(2001)\uff0c\u3008\u907a\u7522\u554f\u984c\u8207\u963f\u62c9\u4f2f\u6578\u5b78\u53f2\u3009\uff0c\u300aHPM\u901a\u8a0a\u300b\u7b2c\u56db\u5377\u7b2c\u4e94\u671f\uff0c\u9801 3-6\u3002<\/p>\n<p style=\"text-align: left;\">\u8a3b \\(2:\\) \u6587\u7ae0\u4e2d\u7528 \\((a,b)\\) \u8868\u793a\u5169\u4eba\u6bd4\u8cfd\u7684\u5c40\u6578\uff0c\u800c \\([A:B]\\) \u4ee3\u8868\u6bd4\u5b8c\u8ced\u91d1\u5206\u914d\u60c5\u5f62\u3002<\/p>\n<p style=\"text-align: left;\">\u8a3b \\(3:\\) \u53ef\u5229\u7528\u7d44\u5408\u516c\u5f0f \\((a+b)^n=\\sum_{k=0}^{n}C_k^na^kb^{n-k}=C_0^na^nb^0+C_1^na^{n-1}b+&#8230;+C_n^na^0b^n\\) \u5c55\u958b\uff0c<\/p>\n<p>\u6216\u76f4\u63a5\u4e58\u958b \\(\\begin{array}{ll}(a+b)^4&amp;=(a+b)^2\\cdot (a+b)^2\\\\&amp;=(a^2+2ab+b^2)(a^2+2ab+b^2)\\\\&amp;=a^4+4a^3b+6a^2b^2+4ab^3+b^4\\end{array}\\)<\/p>\n<hr \/>\n<p style=\"text-align: left;\"><strong>\u53c3\u8003\u6587\u737b <\/strong><\/p>\n<ol>\n<li style=\"text-align: left;\">\u674e\u6587\u6797\u4e3b\u7de8\uff0c\u300a\u6578\u5b78\u73cd\u5bf6\u300b\uff0c\u53f0\u5317\uff1a\u4e5d\u7ae0\u51fa\u7248\u793e\uff0c2000\u5e74\u3002<\/li>\n<li style=\"text-align: left;\">\u6881\u5b97\u5de8\uff0c\u300a\u6578\u5b78\u6b77\u53f2\u5178\u6545\u300b\uff0c\u53f0\u5317\uff1a\u4e5d\u7ae0\u51fa\u7248\u793e\uff0c1995\u5e74\u3002<\/li>\n<li style=\"text-align: left;\">\u6234\u4e45\u6c38\uff0c\u300a\u96a8\u6a5f\u6578\u5b78\u521d\u968e\uff1a\u6dfa\u4ecb\u6a5f\u7387\u8207\u7d71\u8a08\u300b\uff0c\u53f0\u5317\uff1a\u773e\u6587\u5716\u66f8\u51fa\u7248\u793e\uff0c1977\u5e74\u3002<\/li>\n<li style=\"text-align: left;\">Katz\uff0cVictor J.\uff0cA History of Mathematics\uff0cNew York\uff1aAddison Wesley\uff0c1998.<\/li>\n<li style=\"text-align: left;\">Kiernan James F.\uff0c\u201dPoints on the path to probability\u201d\uff0cMathematics Teacher\u00a094\uff1a3\uff0c2001.<\/li>\n<li style=\"text-align: left;\">Salsburg David\u8457\uff0c\u8449\u5049\u6587\u8b6f\uff0c\u300a\u7d71\u8a08\uff0c\u6539\u8b8a\u4e86\u4e16\u754c\u300b\uff08The lady tasting tea\uff1aHow Statistics revolutionized science in the twentieth century\uff09\uff0c\u53f0\u5317\uff1a\u5929\u4e0b\u9060\u898b\u51fa\u7248\u6709\u9650\u516c\u53f8\uff0c2001\u5e74\u3002<\/li>\n<\/ol>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u6a5f\u7387\u6b77\u53f2 (The History of Probability) 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