Quant interview prep: probability, mental math and market-making

The five question types

1. Probability and expected value: dice, coins, cards, conditional probability, Bayes.
2. Mental math: timed arithmetic, fractions, percentages, estimation.
3. Market-making games: quote a bid and ask, update as information arrives.
4. Brainteasers and logic puzzles: structured reasoning under ambiguity.
5. Statistics and coding: regression, distributions, simulations (research and dev roles).

Worked probability examples

• Expected rolls to see a six. Each roll succeeds with probability 1/6, so the expected number of rolls is 6.
• Roll a die, with one optional re-roll. Keep 4, 5 or 6 (each beats the re-roll's average of 3.5); re-roll 1–3. Expected value = (4+5+6)/6 + (3/6)×3.5 = 2.5 + 1.75 = 4.25.
• Expected flips to get two heads in a row. Setting up states gives 6 flips.
• Two children, at least one is a boy. Probability both are boys is 1/3, because the equally likely cases are BB, BG and GB.

Interviewers care about the route: define the random variable, set up the states or cases, and check the answer is plausible. Saying “six feels right because it's the reciprocal of the success probability” is good reasoning to voice before calculating.

Mental math

Many trading firms use timed arithmetic tests, often dozens of questions in a few minutes, followed by quick calculations in conversation. Speed comes from tricks and repetition: multiply by 5 by halving and multiplying by 10, square numbers near 50 or 100 with the difference trick, convert fractions to percentages you know (1/8 = 12.5%), and estimate before calculating so you catch slips. Fifteen minutes of daily drills for a month makes a visible difference.

Market-making games

A typical game: “Make me a market on the sum of two dice.” The expected value is 7, so you might quote 6.5 bid, 7.5 offered. The interviewer then trades with you, reveals information — “one die is a 6” — and expects you to update your quote quickly (the expected sum is now 9.5). They score whether your quotes are centred on fair value, how you size the spread to uncertainty, and whether you update sensibly rather than freezing or overreacting.

Brainteasers

Brainteasers test whether you can structure an unfamiliar problem. Start with small cases, look for a pattern or invariant, and say what you're trying. Getting stuck silently scores worse than a partial answer with clear reasoning. Classic types include weighing problems, river crossings, pirate-gold game theory and estimation questions — see our estimation interview guide.

Mistakes that sink quant candidates

The most common is going silent while calculating; interviewers can't score reasoning they can't hear. Close behind are skipping a sanity check (a probability above one, an expected value outside the possible range), refusing to give an estimate before computing exactly, and freezing in market-making games instead of quoting something sensible and adjusting. Overconfidence hurts too — trading firms value calibrated uncertainty, so “I'm about 70% sure it's 4.25; let me verify the re-roll threshold” is a better habit than false certainty. Finally, candidates over-prepare brainteasers and under-prepare core probability, which carries far more weight.

A four-week plan

• Daily: 15 minutes of timed arithmetic drills.
• Weeks 1–2: probability fundamentals — combinatorics, conditional probability, expectation, Markov chains — 10 problems a day.
• Weeks 2–3: market-making practice with a friend; brainteasers aloud.
• Week 4: mock interviews with time pressure; for research and dev roles, statistics and coding review.

Practising out loud

Quant interviews reward narrated reasoning, which only improves with spoken practice. Explain each probability problem aloud as you solve it, as if the interviewer were listening. A free AI interview assistant like CoPilot Interview can run spoken mock rounds, and its interview report lists likely follow-ups to drill. Pair with our statistics interview questions for research roles.

Disclosure: CoPilot Interview is our product, so weigh what we say about it accordingly. Everything else on this page applies whichever tool you use, or none.

Frequently asked questions

What questions are asked in quant interviews?

Probability and expected value problems, mental arithmetic, market-making games, brainteasers and, for research and developer roles, statistics, modelling and coding questions.

How do I prepare for a quant trading interview?

Drill mental arithmetic daily, solve hundreds of probability problems, practise market-making games with a friend, and do timed mock interviews while narrating your reasoning.

What is a market-making game in an interview?

The interviewer asks you to quote a bid and an ask on an uncertain quantity, such as the sum of two dice, then trades with you and reveals information. They assess fair-value estimation, spread sizing and how you update.

How much math do quant developers need?

Less than traders or researchers, but expect probability basics and expected-value questions alongside heavy coding and systems questions.