Question

An advertising executive studying television viewing habits of married men and women during​ prime-time hours has determined that during prime​ time, husbands are watching television 90 %

of the time. When the husband is watching​ television,60 %

of the time the wife is also watching. When the husband is not watching​ television,20 %

of the time the wife is watching television. Find the probability that if the wife is watching​ television, the husband is also watching television.

What is the probability​ that, if the wife is watching​ television, the husband is also watching​ television?

Answer 1

a) P(wife is watching television) =P(wife is watching television | husband is watching television) * P(husband is watching television) + P(wife is watching television | husband is not watching television) * P(husband is not watching television)

= 0.6 * 0.9 + 0.2 * (1 - 0.9) = 0.56

P(husband is watching television | the wife is watching television)

= P(wife is watching television | husband is watching television) * P(wife is watching television)/P(husband is watching television)

= (0.6 * 0.56)/0.9 = 0.3733