Please show full work especially part C The probability that

Please show full work especially part C

The probability that a man watches a certain television show is 0.4 and the probability that his wife 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 married couple watches the show; a wife watches the show given that her husband does; at least one person of a married couple will watch the show

Solution

Let

H= husband watches
W= wife watches

Thus,

a)

P(H n W) = P(H|W) P(W) = 0.7*0.5 = 0.35 [answer]

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b)

P(W|H) = P(H n W) / P(H) = 0.35/0.4 = 0.875 [answer]

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c)

P(W U H) = P(W) + P(H) - P(W n H) = 0.4 + 0.5 - 0.35 = 0.55 [answer]