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There are 13 ranks of pairs possible with 6 combinations of the suits in each pair. Once a pair has been chosen there are 48 cards left in the deck.

That means 6*13*(48c3) = 1349088 paired hands out of (52c5) total hands, about 52%.

This however also includes the hands with two pair and a full house.

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Q: Calculate the empirical probability of a pair in a 5 card hand of poker?
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