A restaurant manager classifies customers as regular, occasional, or new, and finds that of all customers 50%, 40%, and 10%, respectively, fall into these categories. The manager found that wine was ordered by 70% of the regular customers, by 50% of the occasional customers, and by 30% of the new customers.
a. What is the probability that a randomly chosen customer orders wine?
b. If wine is ordered, what is the probability that the person ordering is a regular customer?
c. If wine is ordered, what is the probability that the person ordering is an occasional customer?