Karen Simpson

2022-01-16

What is the probability that the deal of a five-card hand provides a pair of aces?

Hattie Schaeffer

0.0325
Explanation:
P[odds for one pair] $=C\left(5,2\right)\left(\frac{52}{52}\right)\left(\frac{3}{52}\right)\left(\frac{48}{50}\right)\left(\frac{44}{49}\right)\left(\frac{40}{48}\right)=0.422569$
=42.2569%
A pair of aces is 1/13-th of this $=\frac{0.422569}{13}=0.0325$ (on the condition that there are not more than 2 aces and that there is no pair of three of a kind of another rank)

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