# Question

The application at the beginning of this chapter describes the campaign McDonald’s used several years ago, where customers could win various prizes.

a. Verify the figures that are given in the description. That is, argue why there are 10 winning outcomes and 120 total outcomes.

b. Suppose McDonald’s had designed the cards so that each card had two zaps and three pictures of the winning prize (and again five pictures of other irrelevant prizes). The rules are the same as before: To win, the customer must uncover all three pictures of the winning prize before uncovering a zap. Would there be more or fewer winners with this design? Argue by calculating the probability that a card is a winner.

c. Going back to the original game (as in part a), suppose McDonald’s printed one million cards, each of which was eventually given to a customer. Assume that the (potential) winning prizes on these were: 500,000 Cokes worth $0.40 each, 250,000 French fries worth $0.50 each, 150,000 milk shakes worth $0.75 each, 75,000 hamburgers worth $1.50 each, 20,000 cards with $1 cash as the winning prize, 4000 cards with $10 cash as the winning prize, 800 cards with $100 cash as the winning prize, and 200 cards with $1000 cash as the winning prize. Find the expected amount (the dollar equivalent) that McDonald’s gave away in winning prizes, assuming everyone played the game and claimed the prize if they won. Also find the standard deviation of this amount.

a. Verify the figures that are given in the description. That is, argue why there are 10 winning outcomes and 120 total outcomes.

b. Suppose McDonald’s had designed the cards so that each card had two zaps and three pictures of the winning prize (and again five pictures of other irrelevant prizes). The rules are the same as before: To win, the customer must uncover all three pictures of the winning prize before uncovering a zap. Would there be more or fewer winners with this design? Argue by calculating the probability that a card is a winner.

c. Going back to the original game (as in part a), suppose McDonald’s printed one million cards, each of which was eventually given to a customer. Assume that the (potential) winning prizes on these were: 500,000 Cokes worth $0.40 each, 250,000 French fries worth $0.50 each, 150,000 milk shakes worth $0.75 each, 75,000 hamburgers worth $1.50 each, 20,000 cards with $1 cash as the winning prize, 4000 cards with $10 cash as the winning prize, 800 cards with $100 cash as the winning prize, and 200 cards with $1000 cash as the winning prize. Find the expected amount (the dollar equivalent) that McDonald’s gave away in winning prizes, assuming everyone played the game and claimed the prize if they won. Also find the standard deviation of this amount.

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