How do I approach Statistics & Math interview questions?

Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

What difficulty level is this interview question?

This is a medium difficulty Statistics & Math question, commonly asked during Technical Screen rounds at Citadel.

What role is this question designed for?

This question is commonly asked for Data Scientist candidates at Citadel during technical interviews.

Compute P(third Ace | Ace in first two)

Last updated: Mar 29, 2026

Quick Overview

This question evaluates understanding of conditional probability, dependence versus independence, symmetry arguments, and combinatorial reasoning in sampling without replacement.

Citadel

Oct 13, 2025, 9:49 PM

Data Scientist

Technical Screen

Statistics & Math

Conditional probability with cards drawn without replacement

Problem

You draw three cards without replacement from a standard 52‑card deck (4 Aces). 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 (assume 2 ≤ m < N) contain at least one Ace, what is P(card m+1 is an Ace)?

Solution

Show

Comments (0)

Loading comments...

Browse More Questions

More Statistics & Math•More Citadel•More Data Scientist•Citadel Data Scientist•Citadel Statistics & Math•Data Scientist Statistics & Math