An automobile dealer has kept records on the customers who visited his showroom. Forty percent of the people who visited his dealership were women. Furthermore, his records show that 37% of the women who visited his dealership purchased an automobile, while 21% of the men who visited his dealership purchased an automobile.
a. What is the probability that a customer entering the showroom will buy an automobile?
b. Suppose a customer visited the showroom and purchased a car. What is the probability that the customer was a woman?
c​. ​Suppose a customer visited the showroom but did not purchase a car. What is the probability that the customer was a man?