An automobile dealer has kept records on the customers who visited his showroom. Forty percent of the people who visited his dealership were female. Furthermore, his records show that 45% of the females who visited his dealership purchased an automobile, while 35% of the males who visited his dealership purchased an automobile. Let A, the event that the customer is female. Let A, the event that the customer is male. (a) What is the probability that a customer entering the showroom will buy 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? (Round your answer to three decimal places.)