{"id":104396,"date":"2026-09-12T13:25:32","date_gmt":"2026-09-12T05:25:32","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/104396.html"},"modified":"2026-09-12T13:25:32","modified_gmt":"2026-09-12T05:25:32","slug":"%e6%a6%82%e7%8e%87%e5%85%a5%e9%97%a8%e5%ae%9e%e4%be%8b%ef%bc%9a%e6%9c%89%e8%b6%a3%e7%9a%84%e7%94%9f%e6%97%a5%e6%82%96%e8%ae%ba","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/104396.html","title":{"rendered":"\u6982\u7387\u5165\u95e8\u5b9e\u4f8b\uff1a\u6709\u8da3\u7684\u751f\u65e5\u6096\u8bba"},"content":{"rendered":"

1.\u56e2\u961f\u4e2d\u5927\u6982\u7387\u4f1a\u6709\u540c\u6708\u540c\u65e5\u751f\u7684\u4eba<\/h2>\n

\u5982\u56fe1\u6240\u793a，\u4e00\u652f30\u4eba\u7684\u56e2\u961f\u9996\u6b21\u76f8\u805a\u3002\u5927\u5bb6\u76f8\u805a\u5230\u4e00\u8d77，\u81ea\u7136\u4f1a\u60f3\u5230，\u4f1a\u4e0d\u4f1a\u6709\u4eba\u540c\u6708\u540c\u65e5\u751f？\u4e00\u822c\u4eba\u8ba4\u4e3a\u8fd9\u5e94\u8be5\u662f\u5c0f\u6982\u7387\u4e8b\u4ef6\u5427，\u6bd5\u7adf\u4e00\u5e74\u6709365\u5929，\u8981\u60f3\u4e24\u4e2a\u4eba\u5728\u540c\u4e00\u5929\u751f\u65e5，\u8fd9\u7eaf\u5c5e\u5de7\u5408\u5427？\u7136\u800c，\u8fd9\u5374\u662f\u4e00\u4e2a\u5927\u6982\u7387\u4e8b\u4ef6\u3002\u8981\u60f3\u6253\u597d\u6982\u7387\u7edf\u8ba1\u57fa\u7840，\u5927\u5bb6\u53ef\u4ee5\u53c2\u89c1\u6e05\u534e\u5927\u5b66\u51fa\u7248\u793e\u7684\u300a\u4eba\u4eba\u53ef\u61c2\u7684\u6982\u7387\u7edf\u8ba1\u300b\u3002 \"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

\u56fe1 \u56e2\u961f\u4e2d\u6709\u4eba\u540c\u4e00\u5929\u751f\u65e5\u5417？ \u4ee5"\u81f3\u5c11\u4e24\u4eba\u540c\u6708\u540c\u65e5\u751f"\u4e3a\u4e8b\u4ef6A\u3002\u90a3\u53ef\u4ee5\u662f2\u4eba\u540c\u6708\u540c\u65e5\u751f，\u4e5f\u53ef\u4ee53\u4eba\u540c\u6708\u540c\u65e5\u751f<\/p>\n

\u22ef<\/p>\n

\u22ef<\/p>\n

\\\\cdots\\\\cdots<\/p>\n

<\/span><\/span>\u22ef\u22ef<\/span><\/span><\/span><\/span><\/span>\u3002\u7ecf\u8ba1\u7b97，\u4e00\u652f30\u4eba\u7684\u56e2\u961f\u4e2d，"\u81f3\u5c11\u4e24\u4eba\u540c\u6708\u540c\u65e5\u751f"\u7684\u6982\u7387\u7ea6\u4e3a0.7063；\u4e00\u652f50\u4eba\u7684\u56e2\u961f\u4e2d，"\u81f3\u5c11\u4e24\u4eba\u540c\u6708\u540c\u65e5\u751f"\u7684\u6982\u7387\u7ea6\u4e3a0.9704；\u4e00\u652f70\u4eba\u7684\u56e2\u961f\u4e2d，"\u81f3\u5c11\u4e24\u4eba\u540c\u6708\u540c\u65e5\u751f"\u7684\u6982\u7387\u7ea6\u4e3a0.9992\u3002\u6982\u7387\u503c\u8d8a\u63a5\u8fd1\u4e8e1,\u53ef\u80fd\u6027\u5c31\u8d8a\u5927；\u503c\u4e3a1\u65f6\u8868\u793a\u662f\u5fc5\u7136\u4e8b\u4ef6\u3002\u53ef\u89c1，\u8be5\u4e8b\u4ef6\u771f\u7684\u662f\u5927\u6982\u7387\u4e8b\u4ef6，\u572870\u4eba\u7684\u56e2\u961f\u4e2d\u8be5\u4e8b\u4ef6\u5df2\u63a5\u8fd1\u4e8e\u5fc5\u7136\u3002 \u8fd9\u4e2a\u4e8b\u4ef6\u7684\u6982\u7387\u503c\u662f\u600e\u4e48\u8ba1\u7b97\u51fa\u6765\u7684\u5462？\u4e0b\u9762\u7ed9\u51fa\u601d\u8003\u548c\u8ba1\u7b97\u8fc7\u7a0b\u3002\u7531\u4e8e\u90e8\u5206\u77e5\u8bc6\u8fd8\u6ca1\u5b66\u4e60\u8fc7，\u5982\u679c\u6ca1\u770b\u61c2，\u4ee5\u4e0b\u5185\u5bb9\u53ef\u5148\u8df3\u8fc7\u3002\u53ef\u5728\u540e\u7eed\u5b66\u8fc7\u76f8\u5173\u77e5\u8bc6\u540e\u518d\u56de\u5934\u6765\u9605\u8bfb\u3002 \u6211\u4eec\u7528\u9006\u5411\u601d\u7ef4\u6765\u601d\u8003，\u201c\u81f3\u5c11\u4e24\u4eba\u540c\u6708\u540c\u65e5\u751f"\u7684\u9006\u5411\u4e8b\u4ef6\u5c31\u662f"\u6240\u6709\u4eba\u90fd\u4e0d\u5728\u540c\u4e00\u5929\u8fc7\u751f\u65e5\u201d\u3002\u4e00\u4e2a30\u4eba\u7684\u56e2\u961f，\u8981\u751f\u65e5\u5747\u4e0d\u540c，\u5c31\u662f\u8981\u7528365\u5929\u4e2d\u9009\u51fa30\u4e2a\u65e5\u5b50\u6765\u505a\u7ec4\u5408；\u5982\u679c\u6ca1\u6709\u751f\u65e5\u7ea6\u675f，\u521930\u4e2a\u4eba\u7684\u751f\u65e5\u603b\u7684\u53ef\u80fd\u6027\u6570\u91cf\u5c31\u662f<\/p>\n

365<\/p>\n

30<\/p>\n

365^{30}<\/p>\n

<\/span><\/span>36<\/span>5<\/span><\/span>30<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u79cd\u3002\u636e\u6b64，\u53ef\u8ba1\u7b97\u51fa： <\/p>\n

P<\/p>\n

(<\/p>\n

A<\/p>\n

)<\/p>\n

=<\/p>\n

1<\/p>\n

\u2212<\/p>\n

C<\/p>\n

365<\/p>\n

30<\/p>\n

365<\/p>\n

30<\/p>\n

\u2248<\/p>\n

0.7063<\/p>\n

P(A) = 1 – \\\\frac{\\\\mathbf{C}_{365}^{30}}{365^{30}} \\\\approx 0.7063<\/p>\n

<\/span><\/span>P<\/span>(<\/span>A<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span>36<\/span>5<\/span><\/span>30<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>C<\/span><\/span>365<\/span><\/span><\/span><\/span><\/span>30<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>0.7063<\/span><\/span><\/span><\/span><\/span><\/span> \u540c\u7406，\u53ef\u6c42\u51fa\u572850\u4eba\u7684\u56e2\u961f\u4e2d： <\/p>\n

P<\/p>\n

(<\/p>\n

A<\/p>\n

)<\/p>\n

=<\/p>\n

1<\/p>\n

\u2212<\/p>\n

C<\/p>\n

365<\/p>\n

50<\/p>\n

365<\/p>\n

50<\/p>\n

\u2248<\/p>\n

0.9704<\/p>\n

P(A) = 1 – \\\\frac{\\\\mathbf{C}_{365}^{50}}{365^{50}} \\\\approx 0.9704<\/p>\n

<\/span><\/span>P<\/span>(<\/span>A<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span>36<\/span>5<\/span><\/span>50<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>C<\/span><\/span>365<\/span><\/span><\/span><\/span><\/span>50<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>0.9704<\/span><\/span><\/span><\/span><\/span><\/span> \u572870\u4eba\u7684\u56e2\u961f\u4e2d： <\/p>\n

P<\/p>\n

(<\/p>\n

A<\/p>\n

)<\/p>\n

=<\/p>\n

1<\/p>\n

\u2212<\/p>\n

C<\/p>\n

365<\/p>\n

70<\/p>\n

365<\/p>\n

70<\/p>\n

\u2248<\/p>\n

0.9992<\/p>\n

P(A) = 1 – \\\\frac{\\\\mathbf{C}_{365}^{70}}{365^{70}} \\\\approx 0.9992<\/p>\n

<\/span><\/span>P<\/span>(<\/span>A<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span><\/span>36<\/span>5<\/span><\/span>70<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>C<\/span><\/span>365<\/span><\/span><\/span><\/span><\/span>70<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span><\/span><\/span>0.9992<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

2.\u89e3\u5f00\u56f0\u60d1：\u80fd\u7ed5\u5f00\u5934\u75bc\u7684\u6982\u7387\u516c\u5f0f\u4e0d\u5b66\u4e60\u5417？<\/h2>\n

**（1）\u5b66\u751f\u95ee：**\u8001\u5e08，\u521a\u624d\u60a8\u4e3e\u7684\u5e94\u7528\u573a\u666f\u91cc，\u611f\u89c9\u4e8b\u4ef6\u7684\u9009\u9879\u6570\u9664\u4ee5\u603b\u7684\u9009\u9879\u6570，\u5c31\u53ef\u4ee5\u5f97\u5230\u4e8b\u4ef6\u7684\u6982\u7387，\u5bf9\u5417？ **\u7b80\u8981\u56de\u7b54：**\u53ef\u4ee5\u8fd9\u4e48\u7406\u89e3\u3002\u540e\u7eed\u5b66\u4e60\u66f4\u591a\u7684\u672f\u8bed\u540e，\u53ef\u518d\u7528\u672f\u8bed\u6765\u8868\u8fbe\u3002\u8981\u60f3\u6253\u597d\u6982\u7387\u7edf\u8ba1\u57fa\u7840，\u5927\u5bb6\u53ef\u4ee5\u53c2\u89c1\u6e05\u534e\u5927\u5b66\u51fa\u7248\u793e\u7684\u300a\u4eba\u4eba\u53ef\u61c2\u7684\u6982\u7387\u7edf\u8ba1\u300b\u3002 **（2）\u5b66\u751f\u95ee：**\u8001\u5e08，\u6211\u6bd4\u8f83\u5bb3\u6015\u6982\u7387\u8ba1\u7b97\u7684\u516c\u5f0f，\u770b\u7740\u5c31\u5934\u75bc，\u80fd\u7ed5\u5f00\u4e0d？ **\u7b80\u8981\u56de\u7b54：**\u5efa\u8bae\u4e0d\u8981\u7ed5\u5f00\u3002\u5176\u5b9e\u5e76\u4e0d\u53ef\u6015\u3002\u5176\u4e00，\u6211\u4eec\u53ef\u5c06\u4e8b\u4ef6\u4e4b\u95f4\u7684\u5173\u7cfb\u8fd0\u7b97\u8f6c\u5316\u6210\u96c6\u5408\u7684\u5173\u7cfb\u8fd0\u7b97，\u5c31\u4f1a\u89c9\u5f97\u5bb9\u6613\u8bb8\u591a\u3002\u5176\u4e8c，\u89c9\u5f97\u96be\u7684\u539f\u56e0\u4e0d\u4e00\u5b9a\u662f\u516c\u5f0f\u672c\u8eab，\u6709\u53ef\u80fd\u662f\u5bf9\u5e94\u7528\u573a\u666f\u7684\u7406\u89e3\u6709\u56f0\u96be，\u53ef\u591a\u505a\u7ec3\u4e60\u5f3a\u5316\u7406\u89e3\u3002\u5176\u4e09，\u6982\u7387\u8ba1\u7b97\u6d89\u53ca\u7684\u7b26\u53f7\u3001\u516c\u5f0f\u5e76\u4e0d\u7b97\u591a，\u63d0\u5021\u7528\u56fe\u5f62\u6765\u7406\u89e3，\u53ef\u4ee5\u4f7f\u516c\u5f0f\u66f4\u4e3a\u5f62\u8c61\u3002\u8981\u60f3\u6253\u597d\u6982\u7387\u7edf\u8ba1\u57fa\u7840，\u5927\u5bb6\u53ef\u4ee5\u53c2\u89c1\u6e05\u534e\u5927\u5b66\u51fa\u7248\u793e\u7684\u300a\u4eba\u4eba\u53ef\u61c2\u7684\u6982\u7387\u7edf\u8ba1\u300b\u3002 **（3）\u5b66\u751f\u95ee：**\u8001\u5e08，\u6982\u7387\u5c31\u662f\u4e8b\u4ef6\u5417？\u4e24\u8005\u6709\u4ec0\u4e48\u5173\u8054\u5173\u7cfb？ **\u7b80\u8981\u56de\u7b54：**\u6982\u7387\u548c\u4e8b\u4ef6\u662f\u4e24\u4e2a\u4e0d\u540c\u7684\u672f\u8bed\u3002\u6982\u7387\u7528\u6765\u91cf\u5316\u8868\u8fbe\u4e8b\u4ef6\u53d1\u751f\u7684\u53ef\u80fd\u6027\u3002\u4e8b\u4ef6\u5e38\u7528\u5177\u4f53\u7684\u5e94\u7528\u573a\u666f，\u5e76\u4e14\u5e38\u7528\u96c6\u5408\u8868\u793a\u4e8b\u4ef6\u53d1\u751f\u7684\u7ed3\u679c\u96c6，\u662f\u4e00\u4e2a\u96c6\u5408\u3002\u6982\u7387\u662f\u4e00\u4e2a\u4f4d\u4e8e[0,1]\u7684\u6570\u5b57\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

1.\u56e2\u961f\u4e2d\u5927\u6982\u7387\u4f1a\u6709\u540c\u6708\u540c\u65e5\u751f\u7684\u4eba
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