Banach's matchbox problem

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A classic problem in probability. A pipe smoker has two full boxes of n matches. When he wants a match, he is equally likely to select either box. The question concerns the number of matches left in the second box on the first occasion that he chooses a box and finds it empty. The probability that there are exactly k (k=0, 1, 2,…, n) matches left in the second box is .

Subjects: Probability and Statistics.

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