A standard roulette wheel in the U.S. has the numbers 1 through 36 plus 0 and 00

Question

A standard roulette wheel in the U.S. has the numbers 1 through 36 plus 0 and 00. Of the numbers 1 through 36, 18 are colored red and 18 are colored black. The numbers 0 and 00 are colored green. If a person observes 20 consecutive spins of the wheel, what is the probability that the number of times that the color red occurs is more than 10? You can assume that results of separate spins are independent so that this probability can be modeled using the binomial distribution. HINT: Model using the binomial distribution to first determine n, , and the values of X. Then use MINITAB to find the required probability. When you provide your answer, be sure to state the values of n and that you used as well as the probabilitity requested. HINT: Use cumulative probabilities; cumulative probability is the probability of all values less than or equal to X.

Explanation / Answer

Probability of getting a red color = 18/38

Here number of consecutive throws n = 20

and let's say X is the number of red colors in 20 spins.

so, we want to know

Pr(X >10) = BIN(X >10; 20; 18/38) = 1 - BIN (X<=10; 20 ; 18/38)

NOw it is the format of cumulative distribution.

so  BIN (X<=10; 20 ; 18/38) = 0.6777

Pr(X >10) = 1 - 0.6777 = 0.3223

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