Question

A study was conducted to better understand the television habits of married men and women during prime-time hours. Based on past viewing records, the study determined that during prime time, husbands are watching television 60% of the time. When the husband is watching television, 40% of the time the wife is also watching. When the husband is not watching television, 30% of the time the wife is watching television.
(a) Find the probability that if the wife is watching television, the husband is also watching television.
(b) Find the probability that the wife is watching television during prime time.

Answer 1

Given:- w~ wife , H ~ husband, N~ not

P( husband only watching) = P(H) = 0.6

P( when husband is watching television, wife is also watchingtelevision) = P(W|H) =0.4

P( husband is not watching television, wife is watching television) = P(W|NH) = 0.3

ANSWER:-

A) Probability that if the wife is watching television, the husband is also watching television

= P(H|W) =(0.6×0.4)/(0.6×0.4 + 0.4 × 0.3)

= 0.24/ 0.36

=2/3

B)

Pobability that wife is watching television during prine time = P(w)

P(W|H) = P( H and W) / P(H)

P(W) = P( H and W ) / P( W|H)

Where, P( H and W ) = 0.24 and P(H|W) = 0.67

Therefore, P(W) = 0.24/ 0.67 = 0.36