Both of the first two cards dealt are kings

Question

Two cards are dealt from a shuffled standard $52$ -card deck. Find the probability that both are kings.

Short answer

$1/221$ . The first card is a king with probability $\tfrac{4}{52}$ and then the second with probability $\tfrac{3}{51}$ , giving $\tfrac{12}{2652}=\tfrac{1}{221}$ .

Adapted from Crack, Heard on the Street, Q4.12, p.39; question and answer rewritten by SelfMadeQuant.com.

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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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