Free groceries To attract shoppers, a supermarket runs a weekly contest that involves “scratch-off ” cards. With each purchase, customers get a card with a black spot obscuring a message. When the...

Free groceries To attract shoppers, a supermarket runs a weekly contest that involves “scratch-off ” cards. With each purchase, customers get a card with a black spot obscuring a message. When the spot is scratched away, most of the cards simply say, “Sorry—please try again.” But during the week, 100 customers will get cards that make them eligible for a drawing for free groceries. Ten of the cards say they may be worth $200, 10 others say $100, 20 may be worth $50, and the rest could be worth $20. To register those cards, customers write their names on them and put them in a barrel at the front of the store. At the end of the week, the store manager draws cards at random, awarding the lucky customers free groceries in the amount specified on their card. The drawings continue until the store has given away more than $500 of free groceries. Estimate the average number of winners each week with a simulation.