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Jane Street·Data Scientist·Technical Phone Screen·Intermediate

IntermediatePrefer not to say
May 2026Remote

Summary

Phone screen for a Data Scientist role at Jane Street. One probability question, but it had enough depth to keep me sweating for a while. The kind of problem where you think you see the answer and then realize your intuition was just wrong.

Questions Asked (1)

Q1

You're offered two dice games. Game 1: roll a single die 4 times, win if you get at least one 6. Game 2: roll two dice 24 times, win if at least one roll shows double sixes. Which game gives you a better chance of winning, and why?

Algorithms & Data StructuresProduct Analytics & Metrics
Author's notes

My first instinct was that they're basically the same because the expected number of successes is 2/3 in both cases.

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AI HintsAI Generated

Suggested Approach

Calculate the probability of winning each game by finding the complement of losing (no successful outcome in any trial) and subtracting from 1. Compare the resulting probabilities to determine which game is better, and explain the reasoning clearly.

Pro tip: Mention that this is a classic problem often called the 'Chevalier de Méré' problem, which historically motivated the development of probability theory. This shows depth and connects to the role's quantitative nature.

1. Define the events

For each game, define the success event per trial and the overall win condition. Game 1: success per roll is rolling a 6; win if at least one success in 4 rolls. Game 2: success per roll is rolling double sixes; win if at least one success in 24 rolls.

2. Compute probability of no success in a single trial

Game 1: P(no 6) = 5/6. Game 2: P(no double sixes) = 35/36.

3. Compute probability of no success in all trials

Game 1: (5/6)^4. Game 2: (35/36)^24.

4. Compute win probability

Game 1: 1 - (5/6)^4 ≈ 0.5177. Game 2: 1 - (35/36)^24 ≈ 0.4914.

5. Compare and conclude

Game 1 has a higher probability of winning (≈51.8% vs ≈49.1%). Therefore, Game 1 is better.

Key Points to Mention

  • Use of complementary probability to simplify calculations.
  • Exact formulas: 1 - (5/6)^4 and 1 - (35/36)^24.
  • Numerical approximations to compare: ~0.5177 vs ~0.4914.
  • Explanation that despite more trials in Game 2, the lower per-trial success probability makes it less favorable.
  • Historical context: Chevalier de Méré problem, which led to Pascal and Fermat's work on probability.
  • Clear conclusion: Game 1 is better.

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