5.39 Roulette. An American roulette wheel contains 38 numbers: 18 are red, 18 ar

Question

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 S1 on red. If the ball lands on a red number, you win S1; otherwise you lose your $1. Let X be the amount you win on your S1 bet. Then X is a random variable whose probability distribution is as follows. -1 0.526 P(X=x)| 0.474 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

Explanation / Answer

a) 0.474 + 0.526 = 1

0.474 >= 0 . 0.526 >= 0

hence correct

b)

E(X) = 1 * 0.474 -1*0.526

= -0.052

c) on average we will lose 0.052

d) 100 times = 100 *0.052 = 5.2

1000 times = 52

e) No

as E(X) < 0

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