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Problem 29

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 A technology store holds a contest to attract shoppers. Once an hour, someone at checkout is chosen at random to play in the contest. Here’s how it works: An ace and four other cards are shuffled and placed face down on a table. The customer gets to turn over cards one at a time, looking for the ace. The person wins $\$ 100$of store credit if the ace is the first card,$\$50$ if it is the second card, and $\$ 20, \$10,$ or $\$ 5$if it is the third, fourth, or last card chosen. What is the average dollar amount of store credit given away in the contest? Estimate with a simulation. 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.

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