Being dealt two aces

Question

Two cards are dealt from a well-shuffled standard 52-card deck. Find the probability that both of them are aces.

Short answer

$\tfrac{1}{221}$ . The first card is an ace with probability $\tfrac4{52}$ , and then the second is an ace with probability $\tfrac3{51}$ ; equivalently $\binom42/\binom{52}{2}=6/1326$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question

Conditional Probability, Total Probability, and Bayes' Rule
Worked Examples — Probability Trees, Monty Hall, and Bayesian Updating
Sample Spaces, Events, and the Probability Axioms

Start with a free lesson: Probability Fundamentals is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free