easy   Probability

Poker Pair

A release-checked easy problem for training Cards, Combinations and Permutations, Combinatorics.

Question

A pair in poker is a $5$ card hand where you have $2$ cards of the same rank and $3$ other cards of distinct ranks. Find the probability that a randomly drawn $5$ card poker hand from a standard deck is a pair. Round to the nearest thousandth.

Practice focus

This Probability problem is tagged Cards, Combinations and Permutations, Combinatorics. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.

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