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95% of Republicans are in favor of lowering taxes. 66% of Democrats are in favor of raising taxes. In Texas 78% of people are Republican. If my brother-in-law (from Texas) says he is in favor of raising taxes, what is the probability he is a democrat

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Tundexi

Answer:

The probability that he is a democrat is 0.4583

Step-by-step explanation:

R = Republicans

D = Democrats

L = Favor lowering of taxes

H = Favor increase of taxes

P(L/R) = 0.95

P(H/D) = 0.66

P(R) = 0.78

P(D) = 1 - 0.78 = 0.22

P(D/H) = P (D∩H) / P(H)

P(D/H) = P(H/D) * P(D) / P(H)

P(D/H) = (0.66)(0.22) / {P(H/D).P(D) + P(H/R).P(R)}

P(D/H) = (0.66)(0.22) / (0.66)(0.22) + (0.22)(0.78)

P(D/H) = 0.1452 / 0.1452 + 0.1716

P(D/H) = 0.1452 / 0.3168

P(D/H) = 0.4583333333

P(D/H) = 0.4583

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