Given a standard 52 card deck, what is the expected number of cards needed to draw until we have two cards with the same number?

It's not hard to do for a fixed value (say fix Kings, then deck order can be _K__K__K__K__, all other cards have 1/5 probability of being in each space, so we expect 48*2/5 + 2 = 21.2 cards to be drawn before we find 2 Kings). Is the solution similar when the value is not fixed?


marked as duplicate by Gerry Myerson, Lord Shark the Unknown, Community Oct 15 '18 at 6:52

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