OneMain Financial·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Interviewed for a Data Scientist role at OneMain Financial and got a probability/optimization puzzle that felt deceptively simple at first glance.

Questions Asked (1)

You have 100 red balls and 100 blue balls to distribute across two baskets however you like. One ball is drawn at random from each basket. How do you split the balls to maximize the probability that both draws come up red, and what is that maximum probability?

Algorithms & Data StructuresProduct Analytics & Metrics

Author's notes

I stared at this for a second because my instinct was to split evenly, like 50 red and 50 blue in each basket, and then I realized that gives you 50/100 times 50/100 which is just 25%.

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AI HintsAI Generated

Suggested Approach

Define the probability as the product of the probabilities of drawing a red ball from each basket, then optimize the distribution by considering extreme cases. Recognize that putting a single red ball in one basket and all remaining balls in the other maximizes the product, and compute the resulting probability.

Pro tip: After presenting the solution, mention that this is a classic optimization problem that tests your ability to think probabilistically and consider edge cases, which is directly applicable to A/B testing and risk modeling in data science.

1. Define the probability

Let basket 1 contain r1 red and b1 blue balls, basket 2 contain r2 red and b2 blue balls, with r1+r2=100 and b1+b2=100. The probability of drawing red from both baskets is (r1/(r1+b1)) * (r2/(r2+b2)).

2. Consider extreme distributions

To maximize the product, consider putting all balls of one color in one basket and the other color in the other, or isolating a single red ball. Test the case where one basket has 1 red and 0 blue, and the other has 99 red and 100 blue.

3. Compute the probability for the candidate solution

For basket 1: 1 red, 0 blue → probability of red = 1. For basket 2: 99 red, 100 blue → probability of red = 99/199. The product is 1 * (99/199) = 99/199 ≈ 0.4975.

4. Verify optimality

Argue that any other distribution yields a lower probability. For instance, if both baskets have a mix, the product is less than 0.5, and the extreme case achieves nearly 0.5. Use calculus or logical reasoning to confirm that the maximum occurs at the boundary.

5. State the maximum probability

The maximum probability is 99/199, approximately 0.4975 or 49.75%.

Key Points to Mention

The probability of both draws being red is the product of the individual probabilities.
To maximize the product, one basket should have a probability of 1 (all red balls), which is achieved by putting a single red ball in one basket.
The remaining balls (99 red and 100 blue) go into the other basket, giving a probability of 99/199.
The maximum probability is 99/199 ≈ 0.4975, which is less than 0.5.
This problem illustrates the counterintuitive result that isolating a single red ball maximizes the joint probability.
The solution can be generalized: for n red and n blue balls, the maximum probability is n/(2n-1) when n>1.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.