PracHub
QuestionsPremiumLearningGuidesInterview PrepNEWCoaches
|Home/Statistics & Math/Citadel

Calculate Probability of Third Card Being an Ace

Last updated: Mar 29, 2026

Quick Overview

This question evaluates understanding of conditional probability, dependent events, and combinatorial reasoning within probability theory for a Data Scientist role in the Statistics & Math category.

  • medium
  • Citadel
  • Statistics & Math
  • Data Scientist

Calculate Probability of Third Card Being an Ace

Company: Citadel

Role: Data Scientist

Category: Statistics & Math

Difficulty: medium

Interview Round: Technical Screen

##### Scenario A probability puzzle during a first-round technical screen. ##### Question 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? ##### Hints Condition on the Ace count in the first two draws and apply Bayes.

Quick Answer: This question evaluates understanding of conditional probability, dependent events, and combinatorial reasoning within probability theory for a Data Scientist role in the Statistics & Math category.

Related Interview Questions

  • Solve probability and stopping questions - Citadel (hard)
  • Solve Classic Probability Questions - Citadel (hard)
  • Find constant minimizing absolute error - Citadel (easy)
  • Solve probability and expectation problems - Citadel (hard)
  • Estimate constant under absolute loss - Citadel (easy)
Citadel logo
Citadel
Jul 12, 2025, 6:59 PM
Data Scientist
Technical Screen
Statistics & Math
18
0

Probability Puzzle: Drawing Aces

Setup

  • You draw 3 cards without replacement from a standard 52-card deck (4 Aces, 48 non-Aces).
  • It is known that among the first two cards, there is at least one Ace.

Task

What is the probability that the third card is an Ace, given this information?

Solution

Show

Comments (0)

Sign in to leave a comment

Loading comments...

Browse More Questions

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

Master your tech interviews with 7,500+ real questions from top companies.

Product

  • Questions
  • Learning Tracks
  • Interview Guides
  • Resources
  • Premium
  • For Universities
  • Student Access

Browse

  • By Company
  • By Role
  • By Category
  • Topic Hubs
  • SQL Questions
  • Compare Platforms
  • Discord Community

Support

  • support@prachub.com
  • (916) 541-4762

Legal

  • Privacy Policy
  • Terms of Service
  • About Us

© 2026 PracHub. All rights reserved.