910 A Look Back We introduced sets in the Appendix, and have been using them to represent solutions of equations and inequalities and to represent the domain and range of functions. A Look Ahead Here we discuss methods for counting the number of elements in a set and consider the role of sets in probability. Purchasing a Lottery Ticket In recent years, the jackpot prizes for the nation’s two major multistate lotteries, Mega Millions and Powerball, have climbed to all-time highs. The probability of winning the Mega Millions jackpot is now about 1 in 303 million, and the probability for Powerball is about 1 in 292 million. With such improbable chances of winning the jackpots, one might wonder if there ever comes a point when purchasing a lottery ticket is worthwhile. One important consideration in making this determination is the expected value . For a game of chance, the expected value is a measure of how much a player will win or lose if she or he plays the game a large number of times. The project at the end of this chapter explores the expected value from playing Mega Millions and Powerball and examines how the expected value is related to the jackpot amount. —See Chapter Project— Outline 13. 1 Counting 13. 2 Permutations and Combinations 13. 3 Probability Chapter Review Chapter Test Cumulative Review Chapter Project Counting and Probability 13 Credit: HappyAngel 888/Shutterstock
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