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 35% of the females who visited his dealership purchased an automobile, while 20% of the males who visited his dealership purchased an automobile. Let A1 = the event that the customer is female A2 = 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?
a. 0.26
b. 0.538
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