A record-store owner assesses customers entering the store as high school age, college age, or older, and finds that of all customers 30%, 50%, and 20%, respectively, fall into these categories. The owner also found that purchases were made by 20% of high school age customers, by 60% of college age customers, and by 80% of older customers.
a. What is the probability that a randomly chosen customer entering the store will make a purchase?
b. If a randomly chosen customer makes a purchase, what is the probability that this customer is high school age?