An advertising executive studying television viewing habits of married men and w

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 60% of the time. When the husband is watching television,30%of the time the wife is also watching. When the husband is not watching television,10% of the time the wife is watching television. Find the probability that if the wife is watchingtelevision, the husband is also watching television.

What is the probability that, if the wife is watching television, the husband is also watching television?(Round to three decimal places as needed.)

Explanation / Answer

here probability of  husbands are watching television =P(HW)=0.60

and probability of  husbands are not watching television =P(HWc)=1-0.60=0.40

let probability of wife are watching=P(WW)

probability wife watching given husband watching=P(WW|HW)=0.30

probability wife watching given husband not watching=P(WW|WW) =0.10

probability of wife is watching television=P(WW)=P(HW)*P(WW|HW)+P(HWc)*P(WW|HWc)

=0.6*0.3+0.4*0.1=0.22

hence probability that if the wife is watchingtelevision, the husband is also watching television

=P(HW|WW)=P(HW)*P(WW|HW)/P(WW) =0.6*0.3/0.22=0.818

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