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Public standard problems and original exercises; hidden Trading Interview questions have not been verified.

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Probability and Statistics · Medium

Which Die Was It

Original interpretation · Match confidence: medium

Jane Street · Topic guidance
About this question’s source match

The title and category identify the topic, but no accessible evidence establishes the hidden catalogue statement. This is an original numerical practice question on that specific topic. The hidden Trading Interview wording, parameters and requested subparts have not been verified.

A bag contains a fair four-sided die labeled1..4 and a fair six-sided die labeled1..6. Select one uniformly and keep it. On its first roll you observe4. Which die is more likely? Find both posterior probabilities andP(next roll>4). What if the first observed face were5?

Assumptions and constraints

  • One die chosen once, uniform prior; independent fair rolls conditional on die.
  • Answer every requested subpart and justify your reasoning.

Examples

first observed5
→ six-sided posterior1

The smaller die has zero likelihood.

Company preparation relevance

These links connect this exercise to companies’ public examples or stated interview topics. They do not establish that a company asked this exact Learnr question.

  • Jane Street

    Official topic guidance

    Topic overlap: conditioning in “Given a Seven” (known dice sum),“Liver Disease” (test result),“Which Die Was It” (die identity). The page recommends early clubs/diamonds for interview preparation and identifies conditional probability among their topics.

    Probability Playing Cards — official preparation guidance ↗
    Evidence scope and uncertainty

    Preparation-topic recommendation only. No individual deck card is identified as a match. The page explicitly distinguishes harder cards as recreational. It does not say every card is interview preparation.

    These are Learnr-authored exercises selected for topic overlap. The company does not name these catalogue titles or verify that these exact questions were asked.

References

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Catalogue metadata captured 2026-10-12. Metadata source.