To promote sales a retailer special scratch-coupons. When the shopper makes a purchase, the clerk scratches o↵ the covering to reveal the amount of the discount. The discount is 10%, 30% and 50% of the initial amount. 7/8 of the coupons give the shopper 10%, 3/32 give 30% , and 1/32 give 50%. Suppose that half of the customers purchase a sweater that retails for $100 and another half purchases a suit that retails for $150. What's the probability that a randomly selected customer saves more than $40 by using one of these coupons?