An automobile dealer keeps records on the customers who visi

An automobile dealer keeps records on the customers who visit the showroom. 40% of the people who visited the dealership were female. The records show that 35% of the females who visited his dealership purchased an automobile, while only 20% of the males who visited his dealership purchased an automobile.

a. If a customer who visited the dealership is randomly selected, what is the probability that this customer purchase an automobile?

b. A car salesperson has just informed us that he sold a car to a customer. What is the probability that the customer was female?

Solution

Let

P = purchase

M, F = male, female

Thus,

a)

P(P) = P(M) P(P|M) + P(F) P(P|F)

= (1-0.40)*0.20 + 0.40*0.35

= 0.26 [ANSWER]

*****************

b)

P(F|P) = P(F) P(P|F)/P(P)

= 0.40*0.35/0.26

= 0.538461538 [ANSWER]