# Probability exercise

The probability that a married man watches a certain television show is 0.4, and the probability that a married woman watches the show is 0.5. The probability that a man watches the show, given that his wife does, is 0.7. Find the probability that

(a) a wife watches the show, given that her husband does;

(c) at least one member of a married couple will watch the show.

(a)0.875 (b)0.55

### 2 個解答

• 最佳解答

Denotation :

M = a married man watches the show

W = a married woman watches the show

Given :

P(M) = 0.4

P(W) = 0.5

=====

(a)

P(M | W) = 0.7

P(M and W) | P(W) = 0.7

P(M and W) | 0.5 = 0.7

P(M and W) = 0.35

The required probability

= P(W | M)

= P(M and M) / P(M)

= 0.35/0.4

= 0.875

=====

(b)

The required probability

= P(M or W)

= P(M) + P(W) - P(M and W)

= 0.4 + 0.5 - 0.35

= 0.55

參考資料： 土扁
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• The probability that a married man watches a certain television show is 0.4, and the probability that a married woman watches the show is 0.5. The probability that a man watches the show, given that his wife does, is 0.7. Find the probability that

(a) a wife watches the show, given that her husband does;

(b) at least one member of a married couple will watch the show.

Let M be the event "a married man watches a certain TV show"

P(M)=0.4

Let W be the event "a married woman watches a certain TV show"

P(W)=0.5

P(M|W)=0.7

P(M and W) / P(W) = 0.7

P(M and W) = 0.7 * 0.5 = 0.35

(a)

P(W|M) = P(W and M) / P(M) = 0.35 / 0.4 = 7/8 = 0.875

(b)

P(M or W) = P(M) + P(W) - P(M and W) = 0.4 + 0.5 - 0.35 = 0.55

參考資料： maeducation.edu.hk
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