2. Suppose that n balls are distributed into n boxes so that all of the na possible arrangements are equally likely. We

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2 Suppose That N Balls Are Distributed Into N Boxes So That All Of The Na Possible Arrangements Are Equally Likely We 1 (141.6 KiB) Viewed 48 times

2. Suppose that n balls are distributed into n boxes so that all of the na possible arrangements are equally likely. We would like to compute the probability that only box 1 is empty. Let A be the event that only box 1 is empty. Let B; be the event that box j, j = 2, ..., n, has two balls, box 1 has no balls, and remaining (n - 2) boxes have exactly one ball each. (a) Express A in terms of B;. (5 points) (b) Compute P(B;). (10 points) (c) Compute P(A) from (a) and (b). (10 points)