# Question: An American roulette wheel contains 38 numbers 18 are red

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.

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.

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.

**View Solution:**## Answer to relevant Questions

An investor plans to put $50,000 in one of four investments. The return on each investment depends on whether next year's economy is strong or weak. The following table summarizes the possible payoffs, in dollars, for the ...Let X be the value of a randomly selected decimal digit, that is, a whole number between 0 and 9, inclusive. a. Use simulation to estimate the mean of X. Explain your reasoning. b. Obtain the exact mean of X by applying ...n = 4, p = 0.3, P(X = 2) a. The binomial probability formula, Formula 5.4 Round your probability answers to three decimal places. b. Table VII in Appendix A. Compare your answer here to that in part (a). A student takes a multiple-choice exam with 10 questions, each with four possible selections for the answer. A passing grade is 60% or better. Suppose that the student was unable to find time to study for the exam and just ...A sales representative for a tire manufacturer claims that the company's steel-belted radials last at least 35,000 miles. A tire dealer decides to check that claim by testing eight of the tires. If 75% or more of the eight ...Post your question