2. (30 pts) A standard roulette wheel in the U. S. has the numbers 1 through 36

Question

2. (30 pts) 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 probability requested. Also, see the hint at the end of this page.

Explanation / Answer

There are 18 red colored, 18 black colored and 2 green colored slice of equal chanceson the wheel. Therefore, in a single spin, red color will come with probability 'p'=18/38=9/19. If the wheel is rolled independently, then the outcome is red or not can be compared with a bernoulli trial with success probability p=9/19. Then, out of 20 such spins, if the color red will come X times, then X follows a Binomial distribution with n=20 and p=9/19.

Then probability of occuring 10 or more red outcomes =P[X >= 10] = P[X=10] + P[X=11] + ... + P[X=20].=0.4937186.

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