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Probability 3.0/10

Solution

Full House

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What is the probability that a random 5-card poker hand from a standard 52-card deck is a full house (three of one rank, two of another)? Express as a fraction.

Worked solution

The answer is 6/4165 ≈ 0.00144. Count full houses: choose the trip rank (13 ways) and its suits (C(4,3) = 4), then the pair rank (12 ways) and its suits (C(4,2) = 6): 13·4·12·6 = 3744 hands. Divide by C(52,5) = 2,598,960 to get 3744/2598960 = 6/4165.

Where to go next

Source: Standard poker-hand probability exercise from introductory probability texts. Statement written for AxiomIQ.