Maximize Probability of Drawing Two Red Balls

Quick Overview

This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Maximize Probability of Drawing Two Red Balls states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

Maximize Probability of Drawing Two Red Balls

Company: OneMain Financial

Role: Data Scientist

Category: Statistics & Math

Difficulty: medium

Interview Round: Technical Screen

##### Scenario Distributing 100 red balls and 100 blue balls into two baskets; one ball is drawn from each basket without replacement. ##### Question How should the balls be allocated between the two baskets to maximise the probability that both drawn balls are red? Compute that maximum probability. ##### Hints Let x be red balls in basket A, y in basket B; optimise P(red from A)×P(red from B).

Quick Answer: This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Maximize Probability of Drawing Two Red Balls states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

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Aug 4, 2025, 10:55 AM
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Maximize Probability of Drawing Two Red Balls

Optimize Two-Basket Allocation for Red-Red Draws

Setup

You have 100 red balls and 100 blue balls to distribute between two baskets, A and B. Then you will draw one ball from each basket (no replacement within a basket, but since only one draw is made per basket, replacement is irrelevant).

Task

How should you allocate the balls between the two baskets to maximize the probability that both drawn balls are red? Compute that maximum probability.

Notation Hint

  • Let x = number of red balls in basket A.
  • Let u = number of blue balls in basket A.
  • Then basket B has (100 − x) red and (100 − u) blue.
  • The goal is to maximize P(red from A) × P(red from B).

Clarifying Questions to Ask Guidance

  • Clarify the random variables, distributional assumptions, independence assumptions, and desired output.
  • Show enough derivation for the interviewer to follow the reasoning.
  • Explain how you would validate the result with simulation or sensitivity checks.

What a Strong Answer Covers Guidance

  • A correct setup with definitions, formulas, and boundary conditions.
  • A step-by-step derivation or estimation plan.
  • Interpretation of the result, including uncertainty and practical limitations.
  • Checks for assumptions, edge cases, and numerical stability.

Follow-up Questions Guidance

  • How would the result change if the assumptions were relaxed?
  • Can you verify the answer with a simulation?
  • What is the most likely source of estimation error?
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