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 protable game to play? Explain.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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 protable game to play? Explain.
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