Question: The size of the price discount offered by an industrial marketing manager varies according to order size. During the last quarter, the manager offered price discounts of 20% to one half of his customers and 30% to one-quarter of his customers, and no discount to the rest. He estimates that the probability of receiving a reorder this quarter is 0.90 if the customer received a 20% discount, 0.92 if the customer received a 30% discount, and 0.70 if the customer received no discount.

a) If a customer is selected at random and is observed not to have reordered, what is the probability that this customer was offered no discount last quarter?

b) If a customer is selected at random and is observed to have reordered, what is the probability that this customer was offered a 30% discount last quarter?