Concept explainers
5.39 Roulette. An American roulette wheel contains 38 numbers: 18 are red, 18 are black, and 2 are green. When the roulette wheel is spun, the ball is equally likely to land on any of the 38 numbers. Suppose that you bet $1 on red. If the ball lands on a red number, you win $1; otherwise you lose your $1. Let X be the amount you win on your $1 bet. Then X is a random variable whose probability distribution is as follows.
x | 1 | –1 |
P(X = x) | 0.474 | 0.526 |
- a. Verify that the probability distribution is correct.
- b. Find the expected value of the random variable X.
- c. On average, how much will you lose per play?
- d. Approximately how much would you expect to lose if you bet $1 on red 100 times? 1000 times?
- e. Is roulette a profitable game to play? Explain.
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Introductory Statistics (10th Edition)
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