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Tallest Basketball Player - Answer

The best strategy is to not pick the first boy, then choose the next boy who is taller than the first. The probability is then 11/24 that he will pick the tallest boy.

Let's call the boys: A, B, C and D, tallest to shortest.

If any of them are the first to leave the house, then the probability of picking the tallest boy is 0, 1, 1/2 or 1/3, respectively.

That results in a combined probability of P = (0 + 1 + 1/2 + 1/3) / 4 = 11/24.