已知 P(A|C) = 0.3, P(A|C′) = 0.4, P(B|C) = 0.2, P(B|C′) = 0.3, P(A∩B) = 0.1,
且 A 與 B 獨立, 求 P(C) =?
求統計問題(獨立事件與條件機率)
2013-07-01 8:03 am
回答 (8)
2013-07-01 9:50 am
✔ 最佳答案
P(A)P(B) = 0.1P(A) = P(A|C)P(C)+P(A|C')P(C') = 0.3 P(C)+0.4(1-P(C)) = 0.4 - 0.1 P(C)
P(B) = P(B|C)P(C)+P(B|C')P(C') = 0.2 P(C)+0.3(1-P(C)) = 0.3 - 0.1 P(C)
∴ P(A)-P(B) = 0.1
0.1 = P(A)P(B) = (0.1+P(B))P(B)
==> P(B) = [-0.1+√(0.1^2+4*0.1)]/2 = 0.2701562
P(A) = 0.1+P(B) = 0.3701562
P(C) = (0.4-P(A))/0.1 = 0.298438
2015-01-26 10:35 am
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2015-01-04 5:34 am
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2014-12-02 6:43 am
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原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20130701000016KK00011