An american roulette wheel has 38 slots 18 are red 18 are, Ask an Expert

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An American roulette wheel has 38 slots: 18 are red, 18 are black and 2 are green. Let R be the number of spins until you observe red. Let B be the number of spins until you observe black. Let G be the number of spins until you observe green.

a) What are the distributions and parameters for R, B, and G?

b) How many spins would expect it to take to observe black? How many spins would you expect it to take to observe green?

c) What is the probability that you will observe the first red on the 5th spin?

d) You have a bet with a friend that you can observe 4 blacks in at most 6 spins. What is the probability that you will win this bet?

e) How many spins should you expect it to take to observe 4 blacks? What is the variance of the number of spins that it takes to observe 4 blacks?

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