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?
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
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