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= \uff08P(B|A) * P(A)\uff09\/ P(B)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(1)<\/p>\n\n\n\n<p>\u8fd9\u513f\uff0cA\u3001B\u662f\u4e24\u4e2a\u968f\u673a\u4e8b\u4ef6\uff0cP(A)\u662fA\u53d1\u751f\u7684\u6982\u7387\uff1bP(B)\u662fB\u53d1\u751f\u7684\u6982\u7387\u3002P(A|B)\u3001P(B|A)\uff0c\u79f0\u4e3a\u6761\u4ef6\u6982\u7387\uff1aP(A|B)\u662f\u5728B\u53d1\u751f\u7684\u60c5\u51b5\uff08\u6761\u4ef6\uff09\u4e0bA\u53d1\u751f\u7684\u6982\u7387\uff1bP(B|A)\u662f\u5728A\u53d1\u751f\u7684\u60c5\u51b5\u4e0bB\u53d1\u751f\u7684\u6982\u7387\u3002<\/p>\n\n\n\n<p><strong>\u5e94\u7528\u8d1d\u53f6\u65af\u5b9a\u7406\u7684\u4f8b\u5b50<\/strong><\/p>\n\n\n\n<p>\u53ef\u4ee5\u4ece\u4e24\u4e2a\u89d2\u5ea6\u6765\u89e3\u8bfb\u8d1d\u53f6\u65af\u5b9a\u7406\uff1a\u4e00\u662f\u201c\u8868\u8ff0\u4e86\u4e24\u4e2a\u968f\u673a\u53d8\u91cfA\u548cB\u7684\u76f8\u4e92\u5f71\u54cd\u201d\uff1b\u4e8c\u662f\u201c\u5982\u4f55\u4fee\u6b63\u5148\u9a8c\u6982\u7387\u800c\u5f97\u5230\u540e\u9a8c\u6982\u7387\u201d\uff0c\u4ee5\u4e0b\u5206\u522b\u4e3e\u4f8b\u4e88\u4ee5\u8bf4\u660e\u3002<\/p>\n\n\n\n<p>\u9996\u5148\uff0c\u521d\u7565\u5730\u8bf4\uff0c\u8d1d\u53f6\u65af\u5b9a\u7406(1)\u6d89\u53ca\u4e86\u4e24\u4e2a\u968f\u673a\u53d8\u91cfA\u548cB\uff0c\u8868\u793a\u4e24\u4e2a\u6761\u4ef6\u6982\u7387P(A|B) \u548cP(B|A)\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/p>\n\n\n\n<p>\u4f8b1\uff1a\u67d0\u5c0f\u57ce\u4e00\u6708\u4efd\u6cbb\u5b89\u4e0d\u592a\u597d\uff0c30\u5929\u5185\u53d1\u751f\u5165\u5ba4\u62a2\u52ab\u68486\u8d77\u3002\u8b66\u5bdf\u5c40\u6709\u4e00\u4e2a\u8b66\u62a5\u5668\uff0c\u6709\u4e8b\u53d1\u751f\u65f6\u4fbf\u4f1a\u62c9\u54cd\uff0c\u5305\u62ec\u706b\u707e\u3001\u66b4\u98ce\u96e8\u7b49\u5929\u707e\uff0c\u53ca\u5077\u76d7\u3001\u5f3a\u5978\u4e00\u7c7b\u7684\u4eba\u7978\u3002\u4e00\u6708\u4efd\u65f6\uff0c\u8b66\u62a5\u5668\u6bcf\u5929\u90fd\u54cd\u3002\u5e76\u4e14\uff0c\u4ece\u8fc7\u53bb\u7684\u7ecf\u9a8c\uff0c\u5982\u679c\u6709\u5c45\u6c11\u906d\u5165\u5ba4\u62a2\u52ab\u65f6\uff0c\u8b66\u62a5\u5668\u54cd\u7684\u6982\u7387\u662f0.85\u3002\u73b0\u5728\u4eba\u4eec\u53c8\u542c\u5230\u4e86\u8b66\u62a5\u58f0\uff0c\u90a3\u4e48\uff0c\u8fd9\u6b21\u54cd\u58f0\u4ee3\u8868\u5165\u5ba4\u62a2\u52ab\u7684\u6982\u7387\u662f\u591a\u5c11\u5462\uff1f<\/p>\n\n\n\n<p>\u5206\u6790\u4e00\u4e0b\u8fd9\u4e2a\u95ee\u9898\u3002A: \u5165\u5ba4\u62a2\u52ab\uff1bB: \u62c9\u8b66\u62a5\u3002\u7136\u540e\uff0c\u6211\u4eec\u5df2\u77e5\uff08\u4e00\u6708\u4efd\uff09\uff1a<\/p>\n\n\n\n<p>\u5165\u5ba4\u62a2\u52ab\u7684\u6982\u7387P(A) = 6\/30 = 0.2\uff1b\u62c9\u8b66\u62a5\u7684\u6982\u7387P(B) &nbsp;= 30\/30 = 1\uff1bP(B|A) = \u5165\u5ba4\u62a2\u52ab\u65f6\u62c9\u8b66\u62a5\u7684\u6982\u7387&nbsp;= 0.85\u3002<\/p>\n\n\n\n<p>\u6240\u4ee5\uff0c\u6839\u636e\u516c\u5f0f\uff081\uff09\uff0c\u4ee3\u5165\u5df2\u77e5\u76843\u4e2a\u6982\u7387\uff0c\u8ba1\u7b97\u5f97\u5230 P(A|B) = \uff080.85*0.2\/1\uff09= 0.17\u3002<\/p>\n\n\n\n<p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u8fd9\u6b21\u201c\u8b66\u62a5\u54cd\u7684\u539f\u56e0\u662f\u6709\u4eba\u5165\u5ba4\u62a2\u52ab\u201d\u7684\u6982\u7387\u662f\u767e\u5206\u4e4b\u5341\u4e03\u3002&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p>\u4e0b\u9762\u4e3e\u4f8b\u8bf4\u660e\u5982\u4f55\u7528\u8d1d\u53f6\u65af\u5b9a\u7406\uff0c\u4ece\u201c\u5148\u9a8c\u6982\u7387\u201d\u8ba1\u7b97\u201c\u540e\u9a8c\u6982\u7387\u201d\u3002\u9996\u5148\u5c06\uff081\uff09\u6539\u5199\u4e3a\u5982\u4e0b\u6837\u5b50\uff082\uff09\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1036\" height=\"225\" src=\"http:\/\/dmbok.dama.org.cn\/wordpress\/wp-content\/uploads\/2023\/04\/image-90.png\" alt=\"\" class=\"wp-image-480\"\/><\/figure>\n\n\n\n<p>\u7528\u4e00\u53e5\u8bdd\u6765\u6982\u62ec\uff082\uff09\uff0c\u5b83\u8bf4\u7684\u662f\uff1a\u5229\u7528B\u53d1\u751f\u5e26\u6765\u7684\u65b0\u4fe1\u606f\uff0c\u53ef\u4ee5\u4fee\u6539\u5f53B\u672a\u53d1\u751f\u65f6A\u7684\u201c\u5148\u9a8c\u6982\u7387\u201dP(A)\uff0c\u4ece\u800c\u5f97\u5230B\u53d1\u751f\uff08\u6216\u5b58\u5728\uff09\u65f6\uff0cA\u7684\u201c\u540e\u9a8c\u6982\u7387\u201d\uff0c\u5373P(A|B)\u3002<\/p>\n\n\n\n<p>\u9996\u5148\u7528\u7f8e\u56fd\u5fc3\u7406\u5b66\u5bb6\uff0c2002\u5e74\u8bfa\u8d1d\u5c14\u7ecf\u6d4e\u5956\u5f97\u4e3b\u4e39\u5c3c\u5c14\u00b7\u5361\u5c3c\u66fc\u4e3e\u7684\u4e00\u4e2a\u4f8b\u5b50\u7b80\u5355\u8bf4\u660e\u3002<\/p>\n\n\n\n<p>\u4f8b2\uff1a\u67d0\u57ce\u5e02\u6709\u4e24\u79cd\u989c\u8272\uff08\u84dd\u7eff\uff09\u7684\u51fa\u79df\u8f66\uff1a\u84dd\u8f66\u548c\u7eff\u8f66\u7684\u6bd4\u7387\u662f15:85\u3002\u67d0\u65e5\u67d0\u8f86\u51fa\u79df\u8f66\u591c\u95f4\u8087\u4e8b\u540e\u9003\u9038\uff0c\u4f46\u5f53\u65f6\u6b63\u597d\u6709\u4e00\u4f4d\u76ee\u51fb\u8bc1\u4eba\uff0c\u8fd9\u4f4d\u76ee\u51fb\u8005\u8ba4\u5b9a\u8087\u4e8b\u7684\u51fa\u79df\u8f66\u662f\u84dd\u8272\u7684\u3002\u4f46\u662f\uff0c\u4ed6\u201c\u76ee\u51fb\u7684\u53ef\u4fe1\u5ea6\u201d\u5982\u4f55\u5462\uff1f\u516c\u5b89\u4eba\u5458\u7ecf\u8fc7\u5728\u76f8\u540c\u73af\u5883\u4e0b\u5bf9\u8be5\u76ee\u51fb\u8005\u8fdb\u884c\u201c\u84dd\u7eff\u201d\u6d4b\u8bd5\u800c\u5f97\u5230\uff1a80%\u7684\u60c5\u51b5\u4e0b\u8bc6\u522b\u6b63\u786e\uff0c20%\u7684\u60c5\u51b5\u4e0d\u6b63\u786e\uff0c\u95ee\u9898\u662f\u8ba1\u7b97\u8087\u4e8b\u4e4b\u8f66\u662f\u84dd\u8272\u7684\u51e0\u7387\u3002<\/p>\n\n\n\n<p>\u5047\u8bbeA=\u8f66\u4e3a\u84dd\u8272\u3001B=\u76ee\u51fb\u84dd\u8272\u3002\u9996\u5148\u6211\u4eec\u8003\u8651\u84dd\u7eff\u51fa\u79df\u8f66\u7684\u57fa\u672c\u6bd4\u4f8b\uff0815: 85\uff09\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5728\u6ca1\u6709\u76ee\u51fb\u8bc1\u4eba\u7684\u60c5\u51b5\u4e0b\uff0c\u8087\u4e8b\u4e4b\u8f66\u662f\u84dd\u8272\u7684\u51e0\u7387\u4e3a15%\uff0c\u8fd9\u662f\u201cA=\u84dd\u8f66\u8087\u4e8b\u201d\u7684\u5148\u9a8c\u6982\u7387P(A)= 15%\u3002<\/p>\n\n\n\n<p>\u73b0\u5728\uff0c\u6709\u4e86\u4e00\u4f4d\u76ee\u51fb\u8005\uff0c\u4fbf\u6539\u53d8\u4e86\u4e8b\u4ef6A\u51fa\u73b0\u7684\u6982\u7387\u3002\u76ee\u51fb\u8005\u770b\u5230\u8f66\u662f\u201c\u84dd\u201d\u8272\u7684\u3002\u4e0d\u8fc7\uff0c\u4ed6\u7684\u76ee\u51fb\u80fd\u529b\u4e5f\u8981\u6253\u6298\u6263\uff0c\u53ea\u670980%\u7684\u51c6\u786e\u7387\uff0c\u5373\u4e5f\u662f\u4e00\u4e2a\u968f\u673a\u4e8b\u4ef6\uff08\u8bb0\u4e3aB\uff09\u3002\u6211\u4eec\u7684\u95ee\u9898\u662f\u8981\u6c42\u51fa\u5728\u6709\u8be5\u76ee\u51fb\u8bc1\u4eba\u201c\u770b\u5230\u84dd\u8f66\u201d\u7684\u6761\u4ef6\u4e0b\u8087\u4e8b\u8f66\u201c\u771f\u6b63\u662f\u84dd\u8272\u201d\u7684\u6982\u7387\uff0c\u5373\u6761\u4ef6\u6982\u7387P(A|B)\u3002\u540e\u8005\u5e94\u8be5\u5927\u4e8e\u5148\u9a8c\u6982\u738715%\uff0c\u56e0\u4e3a\u76ee\u51fb\u8005\u770b\u5230\u201c\u84dd\u8f66\u201d\u3002\u5982\u4f55\u4fee\u6b63\u5148\u9a8c\u6982\u7387\uff1f\u9700\u8981\u8ba1\u7b97P(B|A)\u548cP(B)\u3002<\/p>\n\n\n\n<p>\u56e0\u4e3aP(B|A)\u662f\u5728\u201c\u8f66\u4e3a\u84dd\u8272\u201d\u7684\u6761\u4ef6\u4e0b\u201c\u76ee\u51fb\u84dd\u8272\u201d\u7684\u6982\u7387\uff0c\u5373P(B|A) \uff1d80\uff05\u3002\u6982\u7387P(B)\u7684\u8ba1\u7b97\u9ebb\u70e6\u4e00\u70b9\u3002P(B)\u6307\u7684\u662f\u76ee\u51fb\u8bc1\u4eba\u770b\u5230\u4e00\u8f86\u8f66\u4e3a\u84dd\u8272\u7684\u6982\u7387\uff0c\u5e94\u8be5\u7b49\u4e8e\u4e24\u79cd\u60c5\u51b5\u7684\u6982\u7387\u76f8\u52a0\uff1a\u4e00\u79cd\u662f\u8f66\u4e3a\u84dd\u8272\uff0c\u8fa8\u8ba4\u4e5f\u6b63\u786e\uff1b\u53e6\u4e00\u79cd\u662f\u8f66\u4e3a\u7eff\uff0c\u9519\u770b\u6210\u84dd\u3002<\/p>\n\n\n\n<p>\u6240\u4ee5\uff1aP(B) = 15%\u00d780% + 85%\u00d720% = 29%<\/p>\n\n\n\n<p>\u4ece\u8d1d\u53f6\u65af\u516c\u5f0f\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1036\" height=\"151\" src=\"http:\/\/dmbok.dama.org.cn\/wordpress\/wp-content\/uploads\/2023\/04\/image-91.png\" alt=\"\" class=\"wp-image-481\"\/><\/figure>\n\n\n\n<p>\u53ef\u4ee5\u7b97\u51fa\u5728\u6709\u76ee\u51fb\u8bc1\u4eba\u60c5\u51b5\u4e0b\u8087\u4e8b\u8f66\u8f86\u662f\u84dd\u8272\u7684\u51e0\u7387=41%\u3002\u7531\u7ed3\u679c\u53ef\u89c1\uff0c\u88ab\u4fee\u6b63\u540e\u7684\u201c\u8087\u4e8b\u8f66\u8f86\u4e3a\u84dd\u8272\u201d\u7684\u6761\u4ef6\u6982\u738741%\uff0c\u5927\u4e8e\u5148\u9a8c\u6982\u738715%\u5f88\u591a\u3002<\/p>\n\n\n\n<p>\u4f8b3\uff1a\u516c\u5f0f\uff082\uff09\u4e2d\uff0c\u201c\u5148\u9a8c\u201d\u548c\u201c\u540e\u9a8c\u201d \u7684\u5b9a\u4e49\u662f\u4e00\u79cd\u201c\u7ea6\u5b9a\u4fd7\u6210\u201d\uff0c\u662f\u76f8\u5bf9\u800c\u8a00\u7684\uff0c\u524d\u4e00\u6b21\u7b97\u51fa\u7684\u540e\u9a8c\u6982\u7387\uff0c\u53ef\u4f5c\u4e3a\u540e\u4e00\u6b21\u7684\u5148\u9a8c\u6982\u7387\uff0c\u518d\u4e0e\u65b0\u7684\u89c2\u5bdf\u6570\u636e\u76f8\u7ed3\u5408\uff0c\u5f97\u5230\u65b0\u7684\u540e\u9a8c\u6982\u7387\u3002\u56e0\u6b64\uff0c\u8fd0\u7528\u8d1d\u53f6\u65af\u516c\u5f0f\uff0c\u53ef\u4ee5\u5bf9\u67d0\u79cd\u672a\u77e5\u7684\u4e0d\u786e\u5b9a\u6027\u9010\u6b21\u4fee\u6b63\u6982\u7387\u6a21\u578b\u5e76\u5f97\u5230\u6700\u7ec8\u7684\u5ba2\u89c2\u7ed3\u679c\u3002<\/p>\n\n\n\n<p>\u6216\u8005\u53d8\u4e2a\u8bf4\u6cd5\uff0c\u6709\u65f6\u4e5f\u53ef\u4ee5\u8bf4\uff0c\u89c2\u5bdf\u8005\u6839\u636e\u8d1d\u53f6\u65af\u516c\u5f0f\u548c\u4e0d\u65ad\u589e\u52a0\u7684\u6570\u636e\uff0c\u53ef\u80fd\u4fee\u6b63\u81ea\u5df1\u5bf9\u67d0\u4e2a\u4e8b\u4ef6\u7684\u4e3b\u89c2\u201c\u4fe1\u4efb\u5ea6\u201d\u3002<\/p>\n\n\n\n<p>\u4ee5\u629b\u786c\u5e01\u4e3a\u4f8b\uff0c\u4e00\u822c\u8ba4\u4e3a\u786c\u5e01\u662f\u201c\u516c\u5e73\u201d\u7684\u3002\u4f46\u662f\uff0c\u9020\u5047\u7684\u60c5\u51b5\u592a\u591a\uff0c\u7ed3\u679c\u9700\u8981\u8981\u9760\u6570\u636e\u8bf4\u8bdd\u3002<\/p>\n\n\n\n<p>\u6bd4\u5982\u8bf4\uff0c\u8bbe\u547d\u9898A\u4e3a\uff1a\u201c\u8fd9\u662f\u4e00\u4e2a\u516c\u5e73\u786c\u5e01\u201d\uff0c\u89c2\u6d4b\u8005\u5bf9\u6b64\u547d\u9898\u7684\u4fe1\u4efb\u5ea6\u7528P(A)\u8868\u793a\u3002\u5982\u679cP(A)=1\uff0c\u8868\u793a\u89c2\u6d4b\u8005\u575a\u4fe1\u8fd9\u4e2a\u786c\u5e01\u662f\u201c\u6b63\u53cd\u201d\u516c\u5e73\u7684\uff1bP(A)\u8d8a\u5c0f\uff0c\u89c2\u6d4b\u8005\u5bf9\u786c\u5e01\u516c\u5e73\u7684\u4fe1\u4efb\u5ea6\u8d8a\u4f4e\uff1b\u5982\u679cP(A)=0\uff0c\u8bf4\u660e\u89c2\u6d4b\u8005\u575a\u4fe1\u8fd9\u4e2a\u786c\u5e01\u4e0d\u516c\u5e73\uff0c\u6bd4\u5982\u8bf4\uff0c\u662f\u4e00\u4e2a\u9020\u5047\u7684\u3001\u4e24\u9762\u90fd\u6807\u5fd7\u4e3a\u201c\u6b63\u9762\u201d \u7684\u201c\u6b63\u6b63\u201d\u786c\u5e01\u3002\u5982\u679c\u7528B\u8868\u793a\u547d\u9898\u201c\u8fd9\u662f\u4e00\u4e2a\u6b63\u6b63\u786c\u5e01\u201d\u7684\u8bdd\uff0cP(B) = 1- P(A)\u3002<\/p>\n\n\n\n<p>\u4e0b\u9762\u6211\u4eec\u770b\u770b\u5982\u4f55\u6839\u636e\u8d1d\u53f6\u65af\u516c\u5f0f\u6765\u66f4\u65b0\u89c2\u5bdf\u8005\u7684\u201c\u4fe1\u4efb\u5ea6\u201d\u6a21\u578bP(A)\u3002<\/p>\n\n\n\n<p>\u9996\u5148\uff0c\u4ed6\u5047\u8bbe\u4e00\u4e2a\u201c\u5148\u9a8c\u4fe1\u4efb\u5ea6\u201d\uff0c\u6bd4\u5982P(A)=0.9\uff0c0.9\u63a5\u8fd11\uff0c\u8bf4\u660e\u4ed6\u6bd4\u8f83\u504f\u5411\u4e8e\u76f8\u4fe1\u8fd9\u4e2a\u786c\u5e01\u662f\u516c\u5e73\u7684\u3002\u7136\u540e\uff0c\u629b\u786c\u5e011\u6b21\uff0c\u5f97\u5230\u201c\u6b63Head\u201d\uff0c\u4ed6\u6839\u636e\u8d1d\u53f6\u65af\u516c\u5f0f\uff0c\u5c06P(A)\u66f4\u65b0\u4e3aP(A|H)\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1036\" height=\"257\" src=\"http:\/\/dmbok.dama.org.cn\/wordpress\/wp-content\/uploads\/2023\/04\/image-92.png\" alt=\"\" class=\"wp-image-482\"\/><\/figure>\n\n\n\n<p>\u66f4\u65b0\u540e\u7684\u540e\u9a8c\u6982\u7387P(A|H) = 0.82\uff0c\u7136\u540e\uff0c\u518d\u629b\u4e00\u6b21\uff0c\u53c8\u5f97\u5230\u6b63\u9762\uff08H\uff09\uff0c\u4e24\u6b21\u6b63\u9762\u540e\u65b0\u7684\u66f4\u65b0\u503c\u662fP(A|HH) = 0.69\uff0c\u4e09\u6b21\u6b63\u9762\u540e\u7684\u66f4\u65b0\u503c\u662fP(A|HHH) = 0.53\u3002\u5982\u6b64\u629b\u4e0b\u53bb\uff0c\u5982\u679c4\u6b21\u63a5\u8fde\u90fd\u5f97\u5230\u6b63\u9762\uff0c\u65b0\u7684\u66f4\u65b0\u503c\u662fP(A|HHHH) = 0.36\u3002\u8fd9\u65f6\u5019\uff0c\u8fd9\u4f4d\u89c2\u5bdf\u8005\u5bf9\u8fd9\u679a\u786c\u5e01\u662f\u516c\u5e73\u786c\u5e01\u7684\u4fe1\u4efb\u5ea6\u964d\u4f4e\u4e86\u5f88\u591a\uff0c\u4ece\u4fe1\u4efb\u5ea6\u964d\u52300.5\u5f00\u59cb\uff0c\u4ed6\u5c31\u5df2\u7ecf\u6000\u7591\u8fd9\u4e2a\u786c\u5e01\u7684\u516c\u5e73\u6027\uff0c\u63a5\u8fde4\u4e2a\u6b63\u9762\u540e\uff0c\u4ed6\u66f4\u504f\u5411\u4e8e\u8ba4\u4e3a\u8be5\u786c\u5e01\u5f88\u53ef\u80fd\u662f\u4e00\u679a\u4e24\u9762\u90fd\u662f\u6b63\u9762\u7684\u5047\u5e01\uff01<\/p>\n\n\n\n<p>\u4ece\u4e0a\u9762\u51e0\u4e2a\u4f8b\u5b50\uff0c\u6211\u4eec\u521d\u6b65\u4e86\u89e3\u4e86\u8d1d\u53f6\u65af\u5b9a\u7406\u53ca\u5176\u7b80\u5355\u5e94\u7528\u3002<\/p>\n\n\n\n<p><strong>\u8d1d\u53f6\u65af\u5b9a\u7406\u7684\u610f\u4e49<\/strong><\/p>\n\n\n\n<p>\u8d1d\u53f6\u65af\u5b9a\u7406\u662f\u8d1d\u53f6\u65af\u5bf9\u6982\u7387\u8bba\u548c\u7edf\u8ba1\u5b66\u4f5c\u51fa\u7684\u6700\u5927\u8d21\u732e\uff0c\u4f46\u5728\u5f53\u5e74\uff0c\u8d1d\u53f6\u65af\u7684\u201c\u9006\u5411\u6982\u7387\u201d\u7814\u7a76\u548c\u5bfc\u51fa\u7684\u8d1d\u53f6\u65af\u5b9a\u7406\u770b\u8d77\u6765\u5e73\u6de1\u65e0\u5947\uff0c\u672a\u5f15\u4eba\u6ce8\u610f\uff0c\u8d1d\u53f6\u65af\u4e5f\u540d\u4e0d\u89c1\u7ecf\u4f20\u3002\u5982\u4eca\u770b\u6765\u5b8c\u5168\u4e0d\u5e94\u8be5\u662f\u8fd9\u6837\uff0c\u8d1d\u53f6\u65af\u516c\u5f0f\u7684\u91cd\u8981\u610f\u4e49\uff0c\u662f\u5982\u4f8b3\u6240\u793a\u7684\u90a3\u79cd\u63a2\u77e5\u672a\u77e5\u6982\u7387\u7684\u65b9\u6cd5\u3002\u4eba\u4eec\u9996\u5148\u6709\u4e00\u4e2a\u5148\u9a8c\u731c\u6d4b\uff0c\u7136\u540e\u7ed3\u5408\u89c2\u6d4b\u6570\u636e\uff0c\u4fee\u6b63\u5148\u9a8c\uff0c\u5f97\u5230\u66f4\u4e3a\u5408\u7406\u7684\u540e\u9a8c\u6982\u7387\u3002\u8fd9\u5c31\u662f\u8bf4\uff0c\u5f53\u4f60\u4e0d\u80fd\u51c6\u786e\u77e5\u6089\u67d0\u4e2a\u4e8b\u7269\u672c\u8d28\u65f6\uff0c\u4f60\u53ef\u4ee5\u4f9d\u9760\u7ecf\u9a8c\u53bb\u5bf9\u672a\u77e5\u4e16\u754c\u7684\u72b6\u6001\u6b65\u6b65\u903c\u8fd1\uff0c\u4ece\u800c\u5224\u65ad\u5176\u672c\u8d28\u5c5e\u6027\u3002\u5b9e\u9645\u4e0a\uff0c\u5b83\u7684\u601d\u60f3\u4e4b\u6df1\u523b\u8fdc\u51fa\u4e00\u822c\u4eba\u6240\u80fd\u8ba4\u77e5\uff0c\u4e5f\u8bb8\u8d1d\u53f6\u65af\u81ea\u5df1\u751f\u524d\u5bf9\u6b64\u4e5f\u8ba4\u8bc6\u4e0d\u8db3\u3002\u56e0\u4e3a\u5982\u6b64\u91cd\u8981\u7684\u6210\u679c\uff0c\u4ed6\u751f\u524d\u5374\u5e76\u672a\u53d1\u8868\uff0c\u662f\u4ed6\u6b7b\u540e\u76841763\u5e74\uff0c\u624d\u7531\u670b\u53cb\u53d1\u8868\u7684\u3002\u540e\u6765\uff0c\u62c9\u666e\u62c9\u65af\u8bc1\u660e\u4e86\u8d1d\u53f6\u65af\u5b9a\u7406\u7684\u66f4\u666e\u904d\u7684\u7248\u672c\uff0c\u5e76\u5c06\u4e4b\u7528\u4e8e\u5929\u4f53\u529b\u5b66\u548c\u533b\u5b66\u7edf\u8ba1\u4e2d\u3002\u5982\u4eca\uff0c\u8d1d\u53f6\u65af\u5b9a\u7406\u66f4\u662f\u5f53\u4eca\u4eba\u5de5\u667a\u80fd\u4e2d\u5e38\u7528\u7684\u673a\u5668\u5b66\u4e60\u4e4b\u57fa\u7840\u6846\u67b6\u30103\u3011\u3002<\/p>\n\n\n\n<p>\u8d1d\u53f6\u65af\u5b9a\u7406\u4e0e\u5f53\u65f6\u7684\u7ecf\u5178\u7edf\u8ba1\u5b66\u76f8\u6096\uff0c\u751a\u81f3\u663e\u5f97\u6709\u4e9b\u201c\u4e0d\u79d1\u5b66\u201d\u3002\u56e0\u6b64\u5b83\u591a\u5e74\u6765\u4e00\u76f4\u88ab\u96ea\u85cf\uff0c\u4e0d\u53d7\u79d1\u5b66\u5bb6\u5f85\u89c1\u3002\u4ece\u4e0a\u4e00\u8282\u4f8b3\u53ef\u89c1\uff0c\u8d1d\u53f6\u65af\u5b9a\u7406\u7684\u5e94\u7528\u65b9\u6cd5\u662f\u5efa\u7acb\u5728\u4e3b\u89c2\u5224\u65ad\u7684\u57fa\u7840\u4e0a\uff0c\u5148\u4e3b\u89c2\u731c\u6d4b\u4e00\u4e2a\u503c\uff0c\u7136\u540e\u6839\u636e\u7ecf\u9a8c\u4e8b\u5b9e\u4e0d\u65ad\u5730\u4fee\u6b63\uff0c\u6700\u540e\u5f97\u5230\u5ba2\u89c2\u4e16\u754c\u7684\u672c\u8d28\u3002\u5b9e\u9645\u4e0a\uff0c\u8fd9\u6b63\u662f\u79d1\u5b66\u7684\u65b9\u6cd5\uff0c\u4e5f\u662f\u4eba\u7c7b\u4ece\u513f\u7ae5\u5f00\u59cb\uff0c\u8ba4\u77e5\u4e16\u754c\uff08\u5b66\u4e60\uff09\u7684\u65b9\u6cd5\u3002\u6240\u4ee5\u53ef\u4ee5\u8bf4\uff0c\u8fd1\u5e74\u6765\u4eba\u5de5\u667a\u80fd\u7814\u7a76\u7684\u5174\u65fa\u53d1\u8fbe\uff0c\u5173\u952e\u4e4b\u4e00\u662f\u6765\u81ea\u4e8e\u7ecf\u5178\u8ba1\u7b97\u6280\u672f\u548c\u6982\u7387\u7edf\u8ba1\u7684\u201c\u8054\u59fb\u201d\u3002\u800c\u5176\u4e2d\u7684\u8d1d\u53f6\u65af\u516c\u5f0f\u6982\u62ec\u4e86\u4eba\u4eec\u5b66\u4e60\u8fc7\u7a0b\u7684\u539f\u5219\uff0c\u5982\u679c\u914d\u5408\u4e0a\u5927\u6570\u636e\u7684\u8bad\u7ec3\uff0c\u4fbf\u6709\u53ef\u80fd\u66f4\u786e\u5207\u5730\u6a21\u62df\u4eba\u8111\uff0c\u6559\u4f1a\u673a\u5668\u201c\u5b66\u4e60\u201d\uff0c\u4fbf\u80fd\u52a0\u901fAI\u7684\u8fdb\u5c55\u3002\u4ece\u76ee\u524d\u60c5\u51b5\u770b\uff0c\u4e5f\u6b63\u662f\u5982\u6b64\u3002<\/p>\n\n\n\n<p><strong>\u673a\u5668\u5982\u4f55\u5b66\u4e60\uff1f<\/strong><\/p>\n\n\n\n<p>\u6559\u673a\u5668\u5b66\u4e60\uff0c\u5b66\u4e9b\u4ec0\u4e48\u5462\uff1f\u5b9e\u9645\u4e0a\u5c31\u662f\u8981\u5b66\u4f1a\u5982\u4f55\u5904\u7406\u6570\u636e\uff0c\u8fd9\u4e5f\u662f\u5927\u4eba\u6559\u5b69\u5b50\u5b66\u4f1a\u7684\u4e1c\u897f\uff1a\u4ece\u611f\u5b98\u5f97\u5230\u7684\u5927\u91cf\u6570\u636e\u4e2d\u6316\u6398\u51fa\u6709\u7528\u7684\u4fe1\u606f\u6765\u3002\u5982\u679c\u7528\u6570\u5b66\u7684\u8bed\u8a00\u6765\u53d9\u8ff0\uff0c\u5c31\u662f\u4ece\u6570\u636e\u4e2d\u5efa\u6a21\uff0c\u62bd\u8c61\u51fa\u6a21\u578b\u7684\u53c2\u6570\u30104\u3011\u3002<\/p>\n\n\n\n<p>\u673a\u5668\u5b66\u4e60\u7684\u4efb\u52a1\uff0c\u5305\u62ec\u4e86\u201c\u56de\u5f52\u201d\u3001\u201c\u5206\u7c7b\u201d\u3001\u7b49\u4e3b\u8981\u529f\u80fd\u3002\u56de\u5f52\u662f\u7edf\u8ba1\u4e2d\u5e38\u7528\u7684\u65b9\u6cd5\uff0c\u76ee\u7684\u662f\u6c42\u89e3\u6a21\u578b\u7684\u53c2\u6570\uff0c\u4ee5\u4fbf\u201c\u56de\u5f52\u201d\u4e8b\u7269\u7684\u672c\u6765\u9762\u76ee\u3002\u5206\u7c7b\u4e5f\u662f\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u91cd\u8981\u5185\u5bb9\u3002\u5c06\u4e8b\u7269\u201c\u5206\u95e8\u522b\u7c7b\u201d\uff0c\u4e5f\u662f\u4eba\u7c7b\u4ece\u5a74\u513f\u5f00\u59cb\uff0c\u5bf9\u4e16\u754c\u8ba4\u77e5\u7684\u7b2c\u4e00\u6b65\u3002\u5988\u5988\u6559\u7ed9\u5b69\u5b50\uff1a\u8fd9\u662f\u72d7\uff0c\u90a3\u662f\u732b\u3002\u8fd9\u79cd\u5b66\u4e60\u65b9\u6cd5\u5c5e\u4e8e\u201c\u5206\u7c7b\u201d\uff0c\u662f\u5728\u5988\u5988\u7684\u6307\u5bfc\u4e0b\u8fdb\u884c\u7684\u201c\u76d1\u7763\u201d\u5b66\u4e60\u3002\u5b66\u4e60\u4e5f\u53ef\u4ee5\u662f\u201c\u65e0\u76d1\u7763\u201d\u7684\uff0c\u6bd4\u5982\u8bf4\uff0c\u5b69\u5b50\u4eec\u770b\u5230\u4e86\u201c\u5929\u4e0a\u98de\u7684\u9e1f\u3001\u98de\u673a\u201d\u7b49\uff0c\u4e5f\u770b\u5230\u4e86\u201c\u6c34\u4e2d\u6e38\u7684\u9c7c\u3001\u6f5c\u8247\u201d\u7b49\uff0c\u5f88\u81ea\u7136\u5730\u81ea\u5df1\u5c31\u80fd\u5c06\u8fd9\u4e9b\u4e8b\u7269\u5206\u6210\u201c\u98de\u7269\u201d\u548c\u201c\u6e38\u7269\u201d\u4e24\u5927\u7c7b\u3002<\/p>\n\n\n\n<p>\u8d1d\u53f6\u65af\u516c\u5f0f\u4e5f\u53ef\u4ee5\u7528\u6765\u5c06\u6570\u636e\u8fdb\u884c\u5206\u7c7b\uff0c\u4e0b\u4e3e\u4e00\u4f8b\u8bf4\u660e\u3002<\/p>\n\n\n\n<p>\u5047\u8bbe\u6211\u4eec\u6d4b\u8bd5\u4e861000\u4e2a\u6c34\u679c\u7684\u6570\u636e\uff0c\u5305\u62ec\u5982\u4e0b\u4e09\u79cd\u7279\u5f81\uff1a\u5f62\u72b6\uff08\u957f\uff1f\uff09\u3001\u5473\u9053\uff08\u751c\uff1f\uff09\u3001\u989c\u8272\uff08\u9ec4\uff1f\uff09\uff0c\u8fd9\u4e9b\u6c34\u679c\u6709\u4e09\u79cd\uff1a\u82f9\u679c\u3001\u9999\u8549\u3001\u6216\u68a8\u5b50\uff0c\u5982\u56fe2\u6240\u793a\u3002\u73b0\u5728\uff0c\u4f7f\u7528\u4e00\u4e2a\u8d1d\u53f6\u65af\u5206\u7c7b\u5668\uff0c\u5b83\u5c06\u5982\u4f55\u5224\u5b9a\u4e00\u4e2a\u65b0\u7ed9\u7684\u6c34\u679c\u7684\u7c7b\u522b\uff1f\u6bd4\u5982\u8bf4\uff0c\u8fd9\u4e2a\u6c34\u679c\u4e09\u79cd\u7279\u5f81\u5168\u5177\u5907\uff1a\u957f\u3001\u751c\u3001\u9ec4\u3002\u90a3\u4e48\uff0c\u8d1d\u53f6\u65af\u5206\u7c7b\u5668\u5e94\u8be5\u53ef\u4ee5\u6839\u636e\u5df2\u77e5\u7684\u8bad\u7ec3\u6570\u636e\u7ed9\u51fa\u8fd9\u4e2a\u65b0\u6570\u636e\u6c34\u679c\u662f\u6bcf\u79cd\u6c34\u679c\u7684\u6982\u7387\u3002<\/p>\n\n\n\n<p>\u9996\u5148\u770b\u770b\uff0c\u4ece1000\u4e2a\u6c34\u679c\u7684\u6570\u636e\u4e2d\uff0c\u6211\u4eec\u80fd\u5f97\u5230\u4e9b\u4ec0\u4e48\uff1f<\/p>\n\n\n\n<p>1. \u8fd9\u4e9b\u6c34\u679c\u4e2d\uff0c50%\u662f\u9999\u8549\uff0c30%\u662f\u82f9\u679c\uff0c20%\u662f\u68a8\u5b50\u3002\u4e5f\u5c31\u662f\u8bf4\uff0cP(\u9999\u8549) = 0.5\uff0cP(\u82f9\u679c) = 0.3\uff0cP(\u68a8\u5b50) = 0.2\u3002<\/p>\n\n\n\n<p>2. 500\u4e2a\u9999\u8549\u4e2d\uff0c400\u4e2a\uff0880%\uff09\u662f\u957f\u7684\uff0c350\u4e2a\uff0870%\uff09\u662f\u751c\u7684\uff0c450\u4e2a\uff0890%\uff09\u662f\u9ec4\u7684\u3002\u4e5f\u5c31\u662f\u8bf4\uff0cP(\u957f|\u9999\u8549) = 0.8\uff0cP(\u751c|\u9999\u8549) = 0.7\uff0cP(\u9ec4|\u9999\u8549) = 0.9\u3002<\/p>\n\n\n\n<p>3. 300\u4e2a\u82f9\u679c\u4e2d\uff0c&nbsp;0\u4e2a\uff080%\uff09\u662f\u957f\u7684\uff0c150\u4e2a\uff0850%\uff09\u662f\u751c\u7684\uff0c300\u4e2a\uff08100%\uff09\u662f\u9ec4\u7684\u3002\u4e5f\u5c31\u662f\u8bf4\uff0cP(\u957f|\u82f9\u679c) = 0\uff0cP(\u751c|\u82f9\u679c) = 0.5\uff0cP(\u9ec4|\u82f9\u679c) = 1\u3002<\/p>\n\n\n\n<p>4. 200\u4e2a\u68a8\u5b50\u4e2d\uff0c100\u4e2a\uff0850%\uff09\u662f\u957f\u7684\uff0c150\u4e2a\uff0875%\uff09\u662f\u751c\u7684\uff0c50\u4e2a\uff0825%\uff09\u662f\u9ec4\u7684\u3002\u4e5f\u5c31\u662f\u8bf4\uff0cP(\u957f|\u68a8\u5b50) = 0.5\uff0cP(\u751c|\u68a8\u5b50) = 0.75\uff0cP(\u9ec4|\u68a8\u5b50) = 0.25\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0a\u7684\u53d9\u8ff0\u4e2d\uff0cP(A|B)\u8868\u793a\u201c\u6761\u4ef6B\u6210\u7acb\u65f6A\u53d1\u751f\u7684\u6982\u7387\u201d\uff0c\u6bd4\u5982\u8bf4\uff0cP(\u751c|\u68a8\u5b50)\u8868\u793a\u68a8\u5b50\u751c\u7684\u6982\u7387\uff0cP(\u68a8\u5b50|\u751c)\u8868\u793a\u751c\u6c34\u679c\u4e2d\uff0c\u68a8\u5b50\u51fa\u73b0\u7684\u6982\u7387\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"972\" height=\"346\" src=\"http:\/\/dmbok.dama.org.cn\/wordpress\/wp-content\/uploads\/2023\/04\/image-94.png\" alt=\"\" class=\"wp-image-484\"\/><\/figure>\n\n\n\n<p>\u56fe2\uff1a\u8d1d\u53f6\u65af\u5206\u7c7b\u5668<\/p>\n\n\n\n<p>\u6240\u8c13\u201c\u6734\u7d20\u8d1d\u53f6\u65af\u5206\u7c7b\u5668\u201d\uff0c\u5176\u4e2d\u201c\u6734\u7d20\u201d\u4e00\u8bcd\u7684\u610f\u601d\u662f\u8bf4\uff0c\u6570\u636e\u4e2d\u8868\u8fbe\u7684\u4fe1\u606f\u662f\u4e92\u76f8\u72ec\u7acb\u7684\uff0c\u5728\u8be5\u4f8b\u5b50\u7684\u5177\u4f53\u60c5\u51b5\u4e0b\uff0c\u5c31\u662f\u8bf4\uff0c\u6c34\u679c\u7684\u201c\u957f\u3001\u751c\u3001\u9ec4\u201d\u8fd9\u4e09\u9879\u7279\u5f81\u4e92\u76f8\u72ec\u7acb\uff0c\u56e0\u4e3a\u5b83\u4eec\u5206\u522b\u63cf\u8ff0\u6c34\u679c\u7684\u5f62\u72b6\u3001\u5473\u9053\u548c\u989c\u8272\uff0c\u4e92\u4e0d\u76f8\u5173\u3002\u201c\u8d1d\u53f6\u65af\u201d\u4e00\u8bcd\u4fbf\u8868\u660e\u6b64\u7c7b\u5206\u7c7b\u5668\u5229\u7528\u8d1d\u53f6\u65af\u516c\u5f0f\u6765\u8ba1\u7b97\u540e\u9a8c\u6982\u7387\uff0c\u5373\uff1aP(A|\u65b0\u6570\u636e) = P(\u65b0\u6570\u636e|A) P(A)\/ P(\u65b0\u6570\u636e)\u3002<\/p>\n\n\n\n<p>\u8fd9\u513f\u7684\u201c\u65b0\u6570\u636e\u201d = \u201c\u957f\u751c\u9ec4\u201d\u3002\u4e0b\u9762\u5206\u522b\u8ba1\u7b97\u5728\u201c\u957f\u751c\u9ec4\u201d\u6761\u4ef6\u4e0b\uff0c\u8fd9\u4e2a\u6c34\u679c\u662f\u9999\u8549\u3001\u82f9\u679c\u3001\u68a8\u5b50\u7684\u6982\u7387\u3002\u5bf9\u9999\u8549\u800c\u8a00\uff1a<\/p>\n\n\n\n<p>P(\u9999\u8549|\u957f\u751c\u9ec4) = P(\u957f\u751c\u9ec4|\u9999\u8549) P(\u9999\u8549)\/ P(\u957f\u751c\u9ec4)<\/p>\n\n\n\n<p>\u7b49\u5f0f\u53f3\u8fb9\u7b2c\u4e00\u9879\uff1aP(\u957f\u751c\u9ec4|\u9999\u8549) = P(\u957f|\u9999\u8549) * P(\u751c|\u9999\u8549) * P(\u9ec4|\u9999\u8549) = 0.8*0.7*0.9 = 0.504\u3002<\/p>\n\n\n\n<p>\u4ee5\u4e0a\u8ba1\u7b97\u4e2d\uff0c\u5c06P(\u957f\u751c\u9ec4|\u9999\u8549)\u5199\u62103\u4e2a\u6982\u7387\u7684\u4e58\u79ef\uff0c\u4fbf\u662f\u56e0\u4e3a\u7279\u5f81\u4e92\u76f8\u72ec\u7acb\u7684\u539f\u56e0\u3002<\/p>\n\n\n\n<p>\u6700\u540e\u6c42\u5f97\uff1aP(\u9999\u8549|\u957f\u751c\u9ec4) = 0.504*0.5\/ P(\u957f\u751c\u9ec4) = 0.252\/ P(\u957f\u751c\u9ec4)\u3002<\/p>\n\n\n\n<p>\u7c7b\u4f3c\u7684\u65b9\u6cd5\u7528\u4e8e\u8ba1\u7b97\u82f9\u679c\u7684\u6982\u7387\uff1aP(\u957f\u751c\u9ec4|\u82f9\u679c) = P(\u957f|\u82f9\u679c)*P(\u751c|\u82f9\u679c) * P(\u9ec4|\u82f9\u679c) = 0*0.5*1 = 0\u3002P(\u82f9\u679c|\u957f\u751c\u9ec4) = 0\u3002<\/p>\n\n\n\n<p>\u5bf9\u68a8\u5b50\uff1aP(\u957f\u751c\u9ec4|\u68a8\u5b50) = P(\u957f|\u68a8\u5b50)*P(\u751c|\u68a8\u5b50) * P(\u9ec4|\u68a8\u5b50) = 0.5*0.75*0.25 = 0.09375\u3002P(\u68a8\u5b50|\u957f\u751c\u9ec4) = 0.01873\/ P(\u957f\u751c\u9ec4)\u3002<\/p>\n\n\n\n<p>\u5206\u6bcd\uff1aP(\u957f\u751c\u9ec4) = &nbsp;P(\u957f\u751c\u9ec4|\u9999\u8549) P(\u9999\u8549) + P(\u957f\u751c\u9ec4|\u82f9\u679c) P(\u82f9\u679c) + P(\u957f\u751c\u9ec4|\u68a8\u5b50) P(\u68a8\u5b50)= 0.27073<\/p>\n\n\n\n<p>\u6700\u540e\u53ef\u5f97\uff1aP(\u9999\u8549|\u957f\u751c\u9ec4) = 93%<\/p>\n\n\n\n<p>P(\u82f9\u679c|\u957f\u751c\u9ec4) = 0<\/p>\n\n\n\n<p>P(\u68a8\u5b50|\u957f\u751c\u9ec4) = 7%<\/p>\n\n\n\n<p>\u56e0\u6b64\uff0c\u5f53\u4f60\u7ed9\u6211\u4e00\u4e2a\u53c8\u957f\u3001\u53c8\u751c\u3001\u53c8\u9ec4\u7684\u6c34\u679c\uff0c\u6b64\u4f8b\u4e2d\u66fe\u7ecf\u88ab1000\u4e2a\u6c34\u679c\u8bad\u7ec3\u8fc7\u7684\u8d1d\u53f6\u65af\u5206\u7c7b\u5668\u5f97\u51fa\u7684\u7ed3\u8bba\u662f\uff1a\u8fd9\u4e2a\u65b0\u6c34\u679c\u4e0d\u53ef\u80fd\u662f\u82f9\u679c\uff08\u6982\u73870%\uff09\uff0c\u6709\u5f88\u5c0f\u7684\u6982\u7387\uff087%\uff09\u662f\u68a8\u5b50\uff0c\u6700\u5927\u7684\u53ef\u80fd\u6027\uff0893%\uff09\u662f\u9999\u8549\u3002<\/p>\n\n\n\n<p><strong>\u6df1\u5ea6\u5b66\u4e60\u7684\u5965\u79d8<\/strong><\/p>\n\n\n\n<p>\u518d\u770b\u770b\uff0c\u5b69\u5b50\u4eec\u662f\u5982\u4f55\u5b66\u4f1a\u8bc6\u522b\u72d7\u548c\u732b\u7684\uff1f\u662f\u56e0\u4e3a\u5988\u5988\u5e26\u4ed6\u89c1\u8bc6\u4e86\u5404\u79cd\u72d7\u548c\u732b\uff0c\u591a\u6b21\u7684\u7ecf\u9a8c\u4f7f\u4ed6\u8ba4\u8bc6\u4e86\u72d7\u548c\u732b\u7684\u591a\u9879\u7279\u5f81\uff0c\u4ed6\u4fbf\u5f62\u6210\u4e86\u81ea\u5df1\u7684\u5224\u65ad\u65b9\u6cd5\uff0c\u5c06\u5b83\u4eec\u5206\u6210\u201c\u732b\u201d\u3001\u201c\u72d7\u201d\u4e24\u5927\u7c7b\u3002\u79d1\u5b66\u5bb6\u4eec\u4e5f\u7528\u7c7b\u4f3c\u7684\u65b9\u6cd5\u6559\u673a\u5668\u5b66\u4e60\u3002\u6bd4\u5982\u8bf4\uff0c\u4e5f\u8bb8\u53ef\u4ee5\u4ece\u8033\u6735\u6765\u533a\u522b\u732b\u72d7\uff1a\u201c\u72d7\u7684\u8033\u6735\u957f\uff0c\u732b\u7684\u8033\u6735\u77ed\u201d\uff0c\u8fd8\u6709\u201c\u732b\u8033\u6735\u671d\u4e0a\uff0c\u72d7\u8033\u6735\u671d\u4e0b\u201d\u3002\u6839\u636e\u8fd9\u4e24\u4e2a\u67d0\u4e9b\u201c\u732b\u72d7\u201d\u7684\u7279\u5f81\uff0c\u5c06\u5f97\u5230\u7684\u6570\u636e\u753b\u5728\u4e00\u4e2a\u5e73\u9762\u56fe\u4e2d\uff0c\u5982\u56fe3b\u6240\u793a\u3002\u8fd9\u65f6\u5019\uff0c\u6709\u53ef\u80fd\u53ef\u4ee5\u7528\u56fe3b\u4e2d\u7684\u4e00\u6761\u76f4\u7ebfAB\uff0c\u5f88\u5bb9\u6613\u5730\u5c06\u732b\u72d7\u901a\u8fc7\u8fd9\u4e24\u4e2a\u7279\u5f81\u5206\u522b\u5f00\u6765\u3002\u5f53\u7136\uff0c\u8fd9\u53ea\u662f\u4e00\u4e2a\u7b80\u5355\u89e3\u91ca\u201c\u7279\u5f81\u201d\u7684\u4f8b\u5b50\uff0c\u5e76\u4e0d\u4e00\u5b9a\u771f\u80fd\u533a\u5206\u732b\u548c\u72d7\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"972\" height=\"384\" src=\"http:\/\/dmbok.dama.org.cn\/wordpress\/wp-content\/uploads\/2023\/04\/image-95.png\" alt=\"\" class=\"wp-image-485\"\/><\/figure>\n\n\n\n<p>\u56fe3\uff1a\u673a\u5668\u5206\u7c7b<\/p>\n\n\n\n<p>\u603b\u800c\u8a00\u4e4b\uff0c\u673a\u5668\u53ef\u4ee5\u6839\u636e\u67d0\u4e2a\u201c\u7279\u5f81\u201d\uff0c\u5c06\u533a\u57df\u4f5c\u4e00\u4e2a\u7ebf\u6027\u5212\u5206\u3002\u90a3\u4e48\uff0c\u8fd9\u6761\u7ebf\u5e94\u8be5\u753b\u5728\u54ea\u513f\u5462\uff1f\u8fd9\u5c31\u662f\u201c\u8bad\u7ec3\u201d\u8fc7\u7a0b\u9700\u8981\u89e3\u51b3\u7684\u95ee\u9898\u3002\u5728\u673a\u5668\u6a21\u578b\u4e2d\uff0c\u6709\u4e00\u4e9b\u88ab\u79f0\u4e3a\u201c\u6743\u91cd\u201d\u7684\u53c2\u6570w1\u3001w2\u3001w3\uff0c\u2026\u2026\uff0c\u201c\u8bad\u7ec3\u201d\u7684\u8fc7\u7a0b\u5c31\u662f\u8c03\u6574\u8fd9\u4e9b\u53c2\u6570\uff0c\u4f7f\u5f97\u8fd9\u6761\u76f4\u7ebfAB\u753b\u5728\u6b63\u786e\u7684\u4f4d\u7f6e\uff0c\u6307\u5411\u6b63\u786e\u7684\u65b9\u5411\u3002\u4e0a\u8ff0\u201c\u732b\u72d7\u201d\u7684\u4f8b\u5b50\u4e2d\uff0c\u8f93\u51fa\u53ef\u80fd\u662f0\uff0c\u6216\u80051\uff0c\u5206\u522b\u4ee3\u8868\u732b\u548c\u72d7\u3002\u6362\u8a00\u4e4b\uff0c\u6240\u8c13\u201c\u8bad\u7ec3\u201d\uff0c\u5c31\u662f\u5988\u5988\u5728\u6559\u5b69\u5b50\u8ba4\u8bc6\u732b\u548c\u72d7\uff0c\u5bf9AI\u6a21\u578b\u800c\u8a00\uff0c\u5c31\u662f\u8f93\u5165\u5927\u91cf\u201c\u732b\u72d7\u201d\u7684\u7167\u7247\uff0c\u8fd9\u4e9b\u7167\u7247\u90fd\u6807\u8bb0\u4e86\u6b63\u786e\u7684\u7ed3\u679c\uff0cAI\u6a21\u578b\u8c03\u8282\u6743\u91cd\u53c2\u6570\u4f7f\u8f93\u51fa\u7b26\u5408\u5df2\u77e5\u7b54\u6848\u3002<\/p>\n\n\n\n<p>\u7ecf\u8fc7\u8bad\u7ec3\u540e\u7684AI\u6a21\u578b\uff0c\u4fbf\u53ef\u4ee5\u7528\u6765\u8bc6\u522b\u6ca1\u6709\u6807\u8bb0\u7b54\u6848\u7684\u732b\u72d7\u7167\u7247\u4e86\u3002\u4f8b\u5982\uff0c\u5bf9\u4ee5\u4e0a\u6240\u8ff0\u7684\u4f8b\u5b50\uff1a\u5982\u679c\u6570\u636e\u843d\u5728\u76f4\u7ebfAB\u5de6\u8fb9\uff0c\u8f93\u51fa\u201c\u72d7\u201d\uff0c\u53f3\u8fb9\u5219\u8f93\u51fa\u201c\u732b\u201d\u3002<\/p>\n\n\n\n<p>\u56fe3b\u8868\u8fbe\u7684\u662f\u5f88\u7b80\u5355\u7684\u60c5\u5f62\uff0c\u5927\u591a\u6570\u60c5\u51b5\u4e0b\u5e76\u4e0d\u80fd\u7528\u4e00\u6761\u76f4\u7ebf\u5c06\u4e24\u79cd\u7c7b\u578b\u622a\u7136\u5206\u5f00\uff0c\u6bd4\u5982\u56fe4a\u3001\u56fe4b\u3001\u56fe4c\u4e2d\u6240\u793a\u7684\u8d8a\u6765\u8d8a\u590d\u6742\u7684\u60c5\u5f62\uff0c\u6211\u4eec\u5c31\u4e0d\u591a\u8c08\u4e86\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"972\" height=\"299\" src=\"http:\/\/dmbok.dama.org.cn\/wordpress\/wp-content\/uploads\/2023\/04\/image-96.png\" alt=\"\" class=\"wp-image-486\"\/><\/figure>\n\n\n\n<p>\u56fe4\uff1a\u66f4\u591a\u7684\u7279\u5f81\u9700\u8981\u66f4\u591a\u7684\u53c2\u6570\u6765\u8bc6\u522b<\/p>\n\n\n\n<p><strong>\u5224\u522b\u5f0f\u548c\u751f\u6210\u5f0f<\/strong><\/p>\n\n\n\n<p>\u5728\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u76d1\u7763\u5b66\u4e60\u6a21\u578b\uff0c\u53ef\u4ee5\u5206\u4e3a\u4e24\u79cd\uff1a\u5224\u522b\u5f0f\u6a21\u578b\u548c\u751f\u6210\u5f0f\u6a21\u578b\u3002\u4ece\u524d\u9762\u7684\u53d9\u8ff0\u6211\u4eec\u660e\u767d\u4e86\u673a\u5668\u5982\u4f55\u201c\u5206\u7c7b\u201d\u3002\u4ece\u8fd9\u4e24\u79cd\u5b66\u4e60\u65b9\u5f0f\u7684\u540d\u5b57\uff0c\u53ef\u4ee5\u7b80\u5355\u5730\u7406\u89e3\u4e3a\uff1a\u5224\u522b\u5f0f\u6a21\u578b\u66f4\u591a\u662f\u8003\u8651\u5206\u7c7b\u7684\u95ee\u9898\uff0c\u800c\u751f\u6210\u5f0f\u6a21\u578b\u662f\u8981\u4ea7\u751f\u4e00\u4e2a\u7b26\u5408\u8981\u6c42\u7684\u6837\u672c\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"972\" height=\"463\" src=\"http:\/\/dmbok.dama.org.cn\/wordpress\/wp-content\/uploads\/2023\/04\/image-97.png\" alt=\"\" class=\"wp-image-487\"\/><\/figure>\n\n\n\n<p>\u56fe5\uff1a\u5224\u522b\u5f0f\u548c\u751f\u6210\u5f0f\u7684\u533a\u522b<\/p>\n\n\n\n<p>\u8fd8\u7528\u8bc6\u522b\u201c\u732b\u72d7\u201d\u7684\u4f8b\u5b50\uff0c\u7528\u5988\u5988\u6559\u5b69\u5b50\u6765\u6253\u6bd4\u3002\u5988\u5988\u7ed9\u5b69\u5b50\u770b\u4e86\u5f88\u591a\u5f88\u591a\u732b\u548c\u72d7\u6837\u672c\u4e4b\u540e\uff0c\u6307\u7740\u4e00\u53ea\u732b\u95ee\u5b69\u5b50\uff0c\u8fd9\u662f\u5565\uff1f\u5b69\u5b50\u56de\u5fc6\u540e\u4f5c\u51fa\u5224\u65ad\u201c\u662f\u732b\u201d\uff0c\u8fd9\u5c31\u662f\u5224\u522b\u5f0f\u3002\u5b69\u5b50\u7b54\u5bf9\u4e86\u5f88\u9ad8\u5174\uff0c\u81ea\u5df1\u62ff\u8d77\u7b14\uff0c\u5728\u7eb8\u4e0a\u753b\u51fa\u4e00\u4e2a\u8111\u6d77\u4e2d\u732b\u7684\u5f62\u8c61\uff0c\u8fd9\u5c31\u662f\u751f\u6210\u5f0f\u4e86\u3002\u673a\u5668\u7684\u5de5\u4f5c\u4e5f\u7c7b\u4f3c\uff0c\u5982\u56fe5\u6240\u793a\uff0c\u5224\u522b\u5f0f\u4e2d\uff0c\u673a\u5668\u5bfb\u627e\u5224\u522b\u9700\u8981\u7684\u5206\u754c\u7ebf\uff0c\u4ee5\u533a\u5206\u4e0d\u540c\u7c7b\u578b\u7684\u6570\u636e\u5b9e\u4f8b\uff1b\u751f\u6210\u5f0f\u6a21\u578b\u5219\u53ef\u4ee5\u533a\u5206\u72d7\u548c\u732b\uff0c\u6700\u540e\u753b\u51fa\u4e00\u53ea\u201c\u65b0\u7684\u201d\u52a8\u7269\u7167\u7247\uff1a\u72d7\u6216\u732b\u3002<\/p>\n\n\n\n<p>\u7528\u6982\u7387\u7684\u8bed\u8a00\uff1a\u8bbe\u53d8\u91cfY\u4ee3\u8868\u7c7b\u522b\uff0cX\u4ee3\u8868\u53ef\u89c2\u5bdf\u7279\u5f81\u3002\u5224\u522b\u6a21\u578b\u662f\u8ba9\u673a\u5668\u5b66\u4e60\u6761\u4ef6\u6982\u7387\u5206\u5e03P(Y|X)\uff0c\u5373\u5728\u7ed9\u5b9a\u7684\u7279\u5f81X\u4e0b\u7c7b\u522b\u4e3aY\u7684\u6982\u7387\uff1b\u751f\u6210\u6a21\u578b\u4e2d\u673a\u5668\u5bf9\u6bcf\u4e00\u4e2a\u201c\u7c7b\u522b\u201d\u90fd\u5efa\u7acb\u8054\u5408\u6982\u7387P(X,Y)\u7684\u6a21\u578b\uff0c\u56e0\u800c\u53ef\u4ee5\u751f\u6210\u770b\u8d77\u6765\u50cf\u67d0\u79cd\u7c7b\u578b\u7684\u201c\u65b0\u201d\u6837\u672c\u3002<\/p>\n\n\n\n<p>\u4f8b\u5982\uff0c\u7c7b\u522bY\u662f\u201c\u732b\u3001\u72d7\u201d(0,1)\uff0c\u7279\u5f81X\u662f\u8033\u6735\u7684\u201c\u4e0a\u3001\u4e0b\u201d(1,2)\uff0c\u5047\u8bbe\u6211\u4eec\u53ea\u6709\u5982\u56fe\u6240\u793a4\u5f20\u7167\u7247\uff1a(x,y)= {(1,1),(1,0),(2,0),(2,0)}<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"972\" height=\"693\" src=\"http:\/\/dmbok.dama.org.cn\/wordpress\/wp-content\/uploads\/2023\/04\/image-98.png\" alt=\"\" class=\"wp-image-488\"\/><\/figure>\n\n\n\n<p>\u56fe6\uff1a\u5224\u522b\u5f0f\u548c\u751f\u6210\u5f0f\u5efa\u6a21\u7684\u533a\u522b<\/p>\n\n\n\n<p>\u5224\u522b\u5f0f\u7531\u6761\u4ef6\u6982\u7387P(Y|X)\u5efa\u6a21\uff0c\u5f97\u5230\u5206\u754c\u7ebf\uff08\u5de6\u4e0b\u56fe\u4e2d\u7684\u7ea2\u8272\u865a\u7ebf\uff09\uff1b\u751f\u6210\u5f0f\u7531\u8054\u5408\u6982\u7387P(X,Y)\u4e3a\u6bcf\u79cd\u7c7b\u522b\u5efa\u6a21\uff0c\u6ca1\u6709\u5206\u754c\u7ebf\uff0c\u4f46\u5212\u5206\u4e86\u6bcf\u4e2a\u7c7b\u578b\u5728\u6570\u636e\u7a7a\u95f4\u7684\u4f4d\u7f6e\u533a\u95f4\uff08\u53f3\u4e0b\u56fe\u4e2d\u7684\u7ea2\u8272\u5706\u5708\uff09\u3002\u4e24\u79cd\u65b9\u6cd5\u6839\u636e\u4e0d\u540c\u7684\u6a21\u578b\u7ed9\u51fa\u7684\u6982\u7387\u6765\u5de5\u4f5c\u3002\u5224\u522b\u5f0f\u66f4\u7b80\u5355\uff0c\u53ea\u5728\u4e4e\u5206\u754c\u7ebf\uff1b\u800c\u751f\u6210\u5f0f\u6a21\u578b\u8981\u5bf9\u6bcf\u4e2a\u7c7b\u522b\u90fd\u8fdb\u884c\u5efa\u6a21\uff0c\u7136\u540e\u518d\u901a\u8fc7\u8d1d\u53f6\u65af\u516c\u5f0f\u8ba1\u7b97\u6837\u672c\u5c5e\u4e8e\u5404\u7c7b\u522b\u7684\u540e\u9a8c\u6982\u7387\u3002\u751f\u6210\u5f0f\u4fe1\u606f\u4e30\u5bcc\u7075\u6d3b\u6027\u5f3a\uff0c\u4f46\u5b66\u4e60\u548c\u8ba1\u7b97\u8fc7\u7a0b\u590d\u6742\uff0c\u8ba1\u7b97\u91cf\u5927\uff0c\u5982\u679c\u53ea\u505a\u5206\u7c7b\uff0c\u5c31\u6d6a\u8d39\u4e86\u8ba1\u7b97\u91cf\u3002<\/p>\n\n\n\n<p>\u51e0\u5e74\u524d\uff0c\u5224\u522b\u5f0f\u6a21\u578b\u66f4\u53d7\u4eba\u559c\u7231\uff0c\u56e0\u4e3a\u5b83\u7528\u66f4\u76f4\u63a5\u7684\u65b9\u5f0f\u53bb\u89e3\u51b3\u95ee\u9898\uff0c\u65e9\u5c31\u5f97\u5230\u4e86\u4e0d\u5c11\u7684\u5e94\u7528\uff0c\u6bd4\u5982\u5783\u573e\u90ae\u4ef6\u548c\u6b63\u5e38\u90ae\u4ef6\u7684\u5206\u7c7b\u95ee\u9898\u7b49\u30022016\u5e74\u7684alphago \u4e5f\u662f\u5224\u522b\u5f0f\u5e94\u7528\u4f5c\u51b3\u7b56\u7684\u5178\u578b\u4f8b\u5b50\u3002<\/p>\n\n\n\n<p><strong>ChatGPT\u7684\u7279\u70b9<\/strong><\/p>\n\n\n\n<p>\u5982\u679c\u4f60\u8ddfChatGPT\u804a\u8fc7\u5929\uff0c\u4e00\u5b9a\u4f1a\u60ca\u5947\u4e8e\u5b83\u7684\u6d89\u730e\u6781\u5e7f\uff1a\u521b\u4f5c\u8bd7\u6b4c\u3001\u751f\u6210\u4ee3\u7801\u3001\u7ed8\u753b\u4f5c\u56fe\u3001\u64b0\u5199\u8bba\u6587\uff0c\u4f3c\u4e4e\u6837\u6837\u5728\u884c\uff0c\u65e0\u6240\u4e0d\u80fd\u3002\u662f\u4ec0\u4e48\u8d4b\u4e88\u4e86\u5b83\u5982\u6b64\u5f3a\u5927\u7684\u529f\u529b\u5462\uff1f<\/p>\n\n\n\n<p>\u4eceChatGPT\u7684\u540d\u5b57\uff0c\u6211\u4eec\u77e5\u9053\u5b83\u662f\u4e00\u4e2a\u201c\u751f\u6210\u578b\u9884\u8bad\u7ec3\u53d8\u6362\u6a21\u578b\u201d\uff08GPT\uff09\u3002\u8fd9\u91cc\u5305\u62ec\u4e86\u4e09\u4e2a\u610f\u601d\uff1a\u201c\u751f\u6210\u578b\u201c\u3001\u201d\u9884\u8bad\u7ec3\u201c\u3001\u201d\u53d8\u6362\u6a21\u578b\u201d\u3002\u7b2c\u4e00\u4e2a\u8bcd\uff0c\u70b9\u660e\u5b83\u7528\u7684\u6b63\u662f\u4e0a\u9762\u6240\u4ecb\u7ecd\u7684\u751f\u6210\u578b\u5efa\u6a21\u65b9\u6cd5\u3002\u9884\u8bad\u7ec3\uff0c\u8bf4\u7684\u662f\u5b83\u7ecf\u8fc7\u4e86\u591a\u6b21\u8bad\u7ec3\u3002\u53d8\u6362\u6a21\u578b\u662f\u4ece\u201ctransformer\u201d \u7684\u82f1\u6587\u7ffb\u8bd1\u8fc7\u6765\u7684\u3002\u53d8\u6362\u5668transformer 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class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1036\" height=\"247\" src=\"http:\/\/dmbok.dama.org.cn\/wordpress\/wp-content\/uploads\/2023\/04\/image-99.png\" alt=\"\" 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statistics?\u201d\uff0c[J], Nature Biotechnology 22, 1177 &#8211; 1178 (2004) .<\/p>\n\n\n\n<p>3.Jake VanderPlas\uff0c\u201cFrequentism and Bayesianism: A Python-driven Primer\u201d\uff0c[L], arXiv:1411.5018 [astro-ph.IM]\uff0c2014. https:\/\/arxiv.org\/abs\/1411.5018<\/p>\n\n\n\n<p>4.Russell, Stuart; Norvig, Peter (2003) [1995]. 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