an advertising executive is studying television viewing habitsof married men and

Question

an advertising executive is studying television viewing habitsof married men and women during prime-time hours. based on pastviewing records,the executive has determined that during primetime,husbands are watching television 60% of the time. When thehusband is watching television,40% of the time the wife is alsowatching. when the husband is not watching television,30% of thetime the wife is watching television. Find the probability that

A. if the wife is watching television,the husband is alsowatching television

B. the wife is watching television in prime time.

Explanation / Answer

an advertising executive is studying television viewing habitsof married men and women

during prime-time hours. based on past viewing records,theexecutive has determined

that during prime time,husbands are watching television 60% ofthe time. When the

husband is watching television,40% of the time the wife is alsowatching. when the

husband is not watching television,30% of the time the wife iswatching television.

Find the probability that

A. if the wife is watching television,the husband is alsowatching television

LET US CALL THE EVENT OF HUSBAND WATCHING TV AS X.

AND CALL THE EVENT OF HUSBAND NOT WATCHING TV AS X'

P(X) =PROBABILITY OF HUSBAND WATCHING TV = 60%=0.6

P(X')=PROBABILITY OF HUSBAND NOT WATCHING TV= 40%=0.4

WIFE MAY WATCH TV WHEN

1.HUSBAND IS WATCHING WITH 40%=0.4 PROBABILITY

2.WHEN HUSBAND IS NOT WATCHING WITH 30%=0.3 PROBABILITY.

HENCE PROBABILITY OF WIFE WATCHING TV WHEN HUSBAND

IS ALSO WATCHING IS THAT OF CASE 1 = 0.6*0.4=0.24=24%

B. the wife is watching television in prime time.

THIS IS COMBINATION OF 1 AND 2 MENTIONED ABOVE.

HENCE PROBABILITY = 0.6*0.4 (FOR CASE 1)+0.4*0.3 (FOR CASE2)

=0.24+0.12=0.36=36%.

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