# Question

A roulette wheel consists of 38 numbers (18 are red, 18 are black, and 2 are green). Assume that with each spin of the wheel, each number is equally likely to appear.

(a) What is the probability of a gambler winning if he bets on a red number showing up? (b) Suppose the gambler keeps betting on red until he finally wins. Let N be the number of times he plays/ bets. Specify the probability mass function of the random variable N. That is, find PN (k) = Pr (N= k).

(c) Now, suppose the gambler keeps betting on red until he wins twice. Let M be the number of times he plays/ bets. Specify the probability mass function of the random variable M. That is, find PM (k) = Pr (M= k).

(a) What is the probability of a gambler winning if he bets on a red number showing up? (b) Suppose the gambler keeps betting on red until he finally wins. Let N be the number of times he plays/ bets. Specify the probability mass function of the random variable N. That is, find PN (k) = Pr (N= k).

(c) Now, suppose the gambler keeps betting on red until he wins twice. Let M be the number of times he plays/ bets. Specify the probability mass function of the random variable M. That is, find PM (k) = Pr (M= k).

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