A record store owner assesses customers entering the store as high school age, college age,
or older, and finds that among 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) Find the probability that a randomly chosen customer will make a purchase?
(b) If a customer makes a purchase, what is the probability that this customer is of college
age?