Question: A guy randomly picks sticks from three boxes, A, B and C. The sticks he picked, 20% are from A, 37% from B and the

A guy randomly picks sticks from three boxes, A, B and C. The sticks he picked, 20% are from A, 37% from B and the rest from C.

a) Let S be the number of sticks the guy picks until he picks the first one from C. What is the average numberthe guy picks until he picks the first one from C? Whats the distribution, parameter(s) and support of S?

b) What is the probability that the guy picks at least 4 sticks until he picks the first one from C?

c) Let V be the number of sticks the guy picks until he picks the 5th stick that is from B. What is the probability that it he picks exactly 9 sticks until he picks the 5th one from B? what is the distribution and parameter(s) of V?

d) If there is a list of sticks that the guy can pick, 8 from A, 10 from B and 12 from C. He will pick 10 sticks, assume no stick is picked twice. Let W be the number of sticks he picks from A. What is the probability that he picks 3 sticks from A? What is the distribution and parameter(s) of W?

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