Chapter 6.1, Problem 9PB

More Roulette The previous exercise on roulette described two bets: one bet on the single number 23 with winnings of either $350 or - $10 and a different bet on black with winnings of either $10 or - $10. For both types of bets, the expected winning is - $0.53. Which of the two bets has the larger standard deviation? (Hint: Which bet has outcomes that are, on average, further from the mean?) Which bet would you prefer? Explain.

6.8 Roulette A roulette wheel consists of 38 numbers, 0 through 36 and 00. Of these, 18 numbers are red, 18 are black, and 2 are green (0 and 00). You are given $10 and told that you must pick one of two wagers, for an outcome based on a spin of the wheel: (1) Bet $10 on number 23. If the spin results in 23, you win $350 and also get back your $10 bet. If any other number comes up, you lose your $10, or (2) Bet $10 on black. If the spin results in any one of the black numbers, you win $10 and also get back your $10 bet. If any other color comes up, you lose your $10.

1. a. Without doing any calculation, which wager would you prefer? Explain why. (There is no correct answer. Peoples’ choices are based on their individual preferences and risk tolerances.)
2. b. Find the expected outcome for each wager. Which wager is better in this sense?