To boost interest in its big sale, a retailer offers special scratch-off coupons. When the shopper makes a purchase, the clerk scratches off the covering to reveal the amount of the discount. The discount is 10%, 20%, 30%, 40%, or 50% of the initial amount. Most of the coupons are for 10% off, with fewer as the amount of the discount increases. Half of the coupons give the shopper 10% off, 1>4 give 20% off, 1>8 give 30% off, 3>32 give 40% off, and 1>32 give 50% off.
(a) What are your chances of getting more than 30% off of your purchase?
(b) A clerk was surprised—and suspicious—when three shoppers in a row appeared with coupons that gave them half off. Should he have been suspicious?
(c) Half of the customers at a register purchase a sweater that retails for $50 and another half purchase a suit that retails for $200. What is the probability that a customer saves more than $20 by using one of these coupons? Be clear about any assumptions you need to make.