There are B black balls and W white balls in the urn. One ball is repeatedly sampled at random without replacement, until either only black balls or only white balls are left in the urn. (a) Let B = 9 and W = 11. Find the probability that the outcome of the fifth sample is a black ball. (b) Find the probability that the sampling ends with vanishing white ball. (c) Find the average number of sampled balls when the sampling ends with with vanishing white ball. (d) Let B = 999 and W = 1001. Find the probability that the outcome of the fifth sample is a black ball. (e) Find the probability that the sampling ends with vanishing white ball.

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