Probability

👨🏻‍🏫 學術台數學

[匿名]

2010-12-19 1:04 am

For a married couple, probability of husband retired = 0.7, probability of wife retired = 0.4, probability of husband retired given that wife retired = 0.8.
Find probability that :
(a) Both husband and wife are retired.
(b) Only one of them is retired.
(c) Neither of them is retired.
(d) For 2 married couple, find probability that only 1 of the 2 husbands is retired and only 1 of the 2 wives is retired.
[Ans. (a) 0.32 (b) 0.46 (c) 0.22 (d) 0.2016]

更新1:

To : 自由自在 Can you please explain why P(Only one retired) = P(H U W) - P(H ∩ W), thanks.

回答 (2)

用戶9112

2010-12-19 1:33 am

✔ 最佳答案

http://img18.imageshack.us/img18/163/68745693.png

圖片參考：http://img18.imageshack.us/img18/163/68745693.png

2010-12-18 21:16:10 補充：
H∪W是H或W的意思，包含了（只有H）或（只有W）或（H及W同時）已退休的情況。
H∩W是H和W同時已退休，所以H∪W　-　H∩W便餘下只有其中一個已退休的情況。

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myisland8132

2010-12-19 1:36 am

(a) P(Both husband and wife are retired)
=P(husband retired given that wife retired)P(wife retired)
=0.8*0.4
=0.32

(b) First find out P(wife retired given that husband retired)
Since P(wife retired given that husband retired)P(husband retired)
=P(husband retired given that wife retired)P(wife retired)

0.7P(wife retired given that husband retired)=0.32
P(wife retired given that husband retired)=32/70

P(Only one of them is retired)
=0.2*0.4+0.7*(1-32/70)
=0.46

(c) P(Neither of them is retired)
=1-0.32-0.46
=0.22

(d) Since the retired situations of two couple are independent. The required probability is (0.7)(19/35)(0.2)(0.4)+(0.2)(0.4)(0.7)(19/35)+(0.32)(0.22)+(0.22)(0.32)=0.2016

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收錄日期: 2021-04-24 10:07:02
原文連結 [永久失效]:
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