SOLUTION: Radio station WQXP has 15% of the market in Houston and 40% of the market in Dallas. Of the total number of radio listeners in Houston and Dallas, 85% live in Houston and 15% in D

Question 189177: Radio station WQXP has 15% of the market in Houston and 40% of the market in Dallas. Of the total number of radio listeners in Houston and Dallas, 85% live in Houston and 15% in Dallas.
If you know that the listener is indeed listening to station WQXP, what then is the probability that the listener lives in Dallas?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Radio station WQXP has 15% of the market in Houston and 40% of the market in Dallas. Of the total number of radio listeners in Houston and Dallas, 85% live in Houston and 15% in Dallas.
If you know that the listener is indeed listening to station WQXP, what then is the probability that the listener lives in Dallas?
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P(Dallas|WQ) = [P(D and W)] / [P(w and D) + P(W and H)]
= [P(w|D)*P(D)]/{[P(w|D)*P(D)] + [P(W|H)*P(H)]}
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You have P(H) = 0.85 ; P(D) = 0.15 ; P(W|H) = 0.15 ; P(W|D) = 0.40
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Make your substitutions to get the answer.
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This is Bayes way of doing it.
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Cheers,
Stan H.
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