Question

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 married couple watches the show;
(b) a wife watches the show, given that her husband does;
(c) at least one member of a married couple will watch the show.

Answer 1

Let M be the event that a married man watches the show.

Let W be the event that a married woman watches the show.

Given P(M) = 0.4, P(W)=0.5. P(M | W) = 0.7.

$$(a) P(M and W) = P(M | W) P(W) = 0.7(0.5) = 0.35$$

$$(b) P(W | M) = P(M and W)/P(M) = 0.35 / 0.4 = 0.875$$

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