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Exercise 2.19. We have an urn with balls labeled 1,..., 7. Two balls are drawn. Let...

Exercise 2.19. We have an urn with balls labeled 1,..., 7. Two balls are drawn. Let X1 be the number of the first ball drawn and X2 the number of the second ball drawn. By counting favorable outcomes, compute the probabilities P(X 1 = 4), P(X2 = 5), and P(X1 = 4,X 2 = 5) in cases (a) and (b) below.

(a) Write down a precise sum expression for the probability that the first five rolls give a three at most two times.

(b) Calculate the probability that the first three does not appear before the fifth roll.

(c) Calculate the probability that the first three appears before the twentieth roll but not before the fifth roll.

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