Quant interview preparation

Prop market making and quantitative research, weighted the way the interviews actually are: probability and expected value, statistics and machine learning, market making logic, programming and options. Every question is either traced to a named firm from a public candidate report, or tagged at desk level when we could not trace it, and every probability answer shows the reasoning path rather than just the number.

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100 questions, mapped to the firms that asked them

Questions
100
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53
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Updated
September 2026
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All firmsOld Mission Capital12Tower Research Capital10Jump Trading7Akuna Capital5Citadel4D.E. Shaw3Jane Street3AQR Capital Management2DRW2Millennium Management2Schonfeld2Squarepoint Capital2Susquehanna International Group2Belvedere Trading1Optiver1
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  1. 001There are two bags of stones and you do not know how many black or white are in each. You draw two stones and both are black. What is the probability the next one is black, and will you bet on it?ProbabilityHardtechnicalCitadelQuantitative Trading · New York · 2025

    Say this

    Higher than a half, and yes I would bet on black. Because I do not know the composition, the two black draws are evidence about the composition itself, so I update towards bags that are black-heavy. The draws are not independent trials, they are a sample that teaches me about the urn.

    Then walk it

    1. Set it up properly: put a prior over the unknown mixture, say the proportion of black p is uniform on zero to one, and the draws are conditionally independent given p.
    2. Then this is Laplace's rule of succession. With k blacks out of n draws the posterior predictive probability of another black is (k+1)/(n+2). Two blacks out of two gives 3/4.
    3. The intuition without algebra: seeing black twice shifts the posterior mass towards high p, and the predictive probability is the posterior mean of p, which is now above a half.
    4. Compare it with the alternative model. If I were told the bag was exactly 50/50 and I was drawing with replacement, the answer would be exactly a half and the history would be irrelevant. The whole question is which model you are in.
    5. On the betting half: I would take anything better than even money on black, and I would size it small because 3/4 is a function of my prior, not of data. Two draws is almost no information. If the prior were concentrated near a half the answer moves back towards a half.

    Where candidates lose it

    Saying one half because the draws are independent. They are only independent conditional on the unknown composition, and the composition is exactly what you are learning. The second failure is giving 3/4 with no mention of the prior, as if it were a fact rather than the output of a uniform prior you chose.

    Expect next

    • What if the prior were Beta(2,2) instead of uniform?
    • Now make me a market on the probability and I will trade it.
    • Same question but sampling without replacement from a bag of 10 stones. Does the answer move?

    Reported by candidates at Citadel (Quantitative Trading, New York, 2025). Source: Wall Street Oasis.

Firm tags come from public, anonymous candidate reports on Wall Street Oasis: strong signal, not sworn testimony. Firms are named as the places a question was reported, not as partners of Fin Maverick. Answers are written for this page to show how to think out loud; they are not scripts to recite.