1975 USAMO Problems/Problem 5

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Problem

A deck of $n$ playing cards, which contains three aces, is shuffled at random (it is assumed that all possible card distributions are equally likely). The cards are then turned up one by one from the top until the second ace appears. Prove that the expected (average) number of cards to be turned up is $(n+1)/2$.

Solution

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See also

1975 USAMO (ProblemsResources)
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Problem 4
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