Compute P(third Ace | Ace in first two)
Company: Citadel
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
You draw three cards without replacement from a standard 52-card deck. Given that among the first two cards there is at least one Ace, what is the probability that the third card is an Ace? State and justify any independence or symmetry arguments you use. Then generalize: for a deck of N cards with A Aces, given that the first m cards (m ≥ 2) contain at least one Ace, what is P(card m+1 is an Ace)?
Quick Answer: This question evaluates understanding of conditional probability, dependence versus independence, symmetry arguments, and combinatorial reasoning in sampling without replacement.