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[Core] Probability 問題 (conditional probability)

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Probability 問題 (conditional probability)

In a building, the probability of a husband and a wife with a degree is 0.3 and 0.2 respectively , and it is known that the probability of a husband with a degree given that a wife has a degree is 0.9. If a married couple is chosen at random, find

1) probability that a wife has a degree given that the husband has a degree (ans: 0.6)
2) neither of them has a degree given that the wife doesn't have a degree (ans: 0.85)
3) husband doesn't have a degree given that only one of them has a degree (ans: 0.1429)
   

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P(H) = 0.3
P(W) = 0.2
P(H | W) = 0.9
P(H and W) = 0.2*0.9 = 0.18
Thus we have the table
                H                H'                Total
W                0.18        0.02        0.20
W'                0.12        0.68        0.80
Total        0.30        0.70        1.00
(a) The required probability = 0.18/0.30 = 0.6
(b) The required probability = 0.68/0.80 = 0.85
(c) The required probability = 0.02/(0.02+0.12) = 0.142857

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thxxx

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