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 easy difficulty Statistics & Math question, commonly asked during HR Screen rounds at Jane Street.

What role is this question designed for?

This question is commonly asked for Software Engineer candidates at Jane Street during technical interviews.

Calculate dice game win probability | Jane Street Interview Question

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 Calculate dice game win probability states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

Calculate dice game win probability

Dice Game With Tie Rerolls: Probability You Eventually Win

Context

Three players each roll a fair standard 6-sided die.
The highest roll wins.
If there is a tie for the highest number, only the tied players re-roll; this repeats until there is a single winner.

Question

Your two friends have both rolled a 4. You now roll next. What is the probability that you eventually win the game?

Constraints & Assumptions

Preserve the scope, facts, inputs, and requested outputs from the prompt above.
If the prompt leaves a detail unspecified, state a reasonable assumption before relying on it.
Keep the answer interview-ready: concise enough to present, but concrete enough to implement or evaluate.

Clarifying Questions to Ask

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

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

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?

Quick Overview

Question

Your two friends have both rolled a 4. You now roll next. What is the probability that you eventually win the game?

Constraints & Assumptions

Preserve the scope, facts, inputs, and requested outputs from the prompt above.

If the prompt leaves a detail unspecified, state a reasonable assumption before relying on it.

Keep the answer interview-ready: concise enough to present, but concrete enough to implement or evaluate.

Clarifying Questions to Ask

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

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

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?

Calculate dice game win probability

Quick Overview

Calculate dice game win probability

Calculate dice game win probability

Dice Game With Tie Rerolls: Probability You Eventually Win

Context

Question

Constraints & Assumptions

Clarifying Questions to Ask

What a Strong Answer Covers

Follow-up Questions

Write your answer

Calculate dice game win probability

Quick Overview

Calculate dice game win probability

Calculate dice game win probability

Dice Game With Tie Rerolls: Probability You Eventually Win

Context

Question

Constraints & Assumptions

Clarifying Questions to Ask

What a Strong Answer Covers

Follow-up Questions

Write your answer