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Given a standard 52 card deck, with 5 players in a five card draw poker game, one particular player ends up holding the queen of hearts while another particular player has a hand with a two, any suite, in theirs. What are the odds of this happening?

Obviously the first round, everyone gets 5 cards. So, first calculate the odds that our first target player gets the queen of hearts and/or the second particular player gets any two. Neither has to get their card during the first round, but could get them after turning in cards.

Then calculate the odds of one or both cards showing up on the second round after players turn in cards. This will probably crate a range for the odds.

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  • I don't think this question is answerable as is. You would need to know the probabilities of players replacing cards and how many. As you point out it can be calculated for the first 5 cards dealt to each player, but there are far too many unknown variables to provide an answer after the draw.
    – TTT
    Dec 8 '21 at 17:40

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