Two aces in a row

What this conditional-probability interview question tests

This is a foundational probability question that appears in early-stage interviews at quant firms. It tests whether you can correctly reason about sampling without replacement — a scenario where each draw changes the composition of the remaining population, and thus the probability of subsequent events.

The key skill is recognizing that the probability of the second draw depends on the outcome of the first. Candidates should set up the problem by identifying the total number of cards, the number of aces, and how both quantities shift after the first draw. Clean, explicit reasoning about conditional probabilities matters more than speed.

• Independence vs. dependence in sequential events
• Multiplication rule for dependent events
• Counting and combinatorial setup