Probability exercise

Denotation :
M = a married man watches the show
W = a married woman watches the show

Given :
P(M) = 0.4
P(W) = 0.5


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(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


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(b)
The required probability
= P(M or W)
= P(M) + P(W) - P(M and W)
= 0.4 + 0.5 - 0.35
= 0.55

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