求統計問題(獨立事件與條件機率)

👨🏻‍🏫 學術台數學

[匿名]

2013-07-01 8:03 am

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) =?

回答 (8)

老怪物

2013-07-01 9:50 am

✔ 最佳答案

P(A)P(B) = 0.1
P(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

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[匿名]

2015-01-26 10:35 am

試試看他的方法
TS777.CC

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Chester

2015-01-04 5:34 am

看看他的答案
TS777.CC

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[匿名]

2014-12-02 6:43 am

他的答案你會滿意的
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