Exactly two aces in a thirteen-card hand

Question

Thirteen cards are dealt from a thoroughly shuffled standard $52$ -card deck. Find, to two decimal places, the probability that the hand contains precisely two aces.

Short answer

About $0.21$ . The ace count is hypergeometric: $\binom42\binom{48}{11}/\binom{52}{13}\approx0.2135$ .

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Lessons behind this question

Counting and Combinatorics
Sample Spaces, Events, and the Probability Axioms
Conditional Probability, Total Probability, and Bayes' Rule

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