Question

2. Suppose that 52% of the customers of a particular car dealership are men and the remaining 48% are women. The marketing office wants to be able to predict the gender of individual buyers. You know from historical data at the dealership that 5% of male buyers choose Trim Package l and that 10% of female buyers choose Trim Package l when buying a new car from your dealership. Given that a new car was sold with Trim Package 1, what is the probability that the buyer was a man?

Please show all work and steps!

Answer 1

M - Male

F- Female

X - Trim package

P(M) = 0.52 , P(F) = 0.48 , P(X|M) = 0.05 , (X|F) = 0.10

P(M|X) = P( and X) /P(X)

= 0.05 * 0.52 /(0.05 * 0.52 + 0.10 * 0.48)

= 0.35135135135