Fast Quant Interview Drill Session

Reviewed by Fallon Han· Updated 2026-06-01 21:30:02.143

This conversation was generated using Cook'd AI's career assistant and reviewed by Fallon Han from our editorial team for accuracy.

I am a third-year statistics student in the US on an F-1 visa, and I want a technically intense interview simulation for a quant trading internship at a prop shop. I do not want classic finance questions. Can you run me through rapid probability puzzles and brainteasers like I would get in a real interview?

Absolutely. I will keep it close to a prop trading screen: fast, verbal, and math-heavy. We will focus on three things: 1. Quick probability setup 2. Clean mental math and approximation 3. Explaining your logic under time pressure First question: You flip a fair coin repeatedly until you see two heads in a row. What is the expected number of flips? Give me your answer and then walk me through the reasoning out loud, as if I am interrupting you.

My first instinct is 6, because I remember similar coin-streak questions often land there. I would try to solve it by setting states: one state for no prior head, one state for one head in a row, and then write equations for the expected flips from each state.

Good instinct. The state approach is exactly what I want. Let E0 be the expected flips from a clean start, and E1 be the expected flips when you already have one head in a row. You can build: E0 = 1 + 0.5 E1 + 0.5 E0 E1 = 1 + 0.5 E1 + 0.5 E0? Not quite. Now correct that carefully. From the one-head state, if the next flip is heads, you stop. If tails, you reset. Say the equations cleanly and solve them. I am looking for speed and accuracy, not just the final number.

From E0, after one flip, with probability 1/2 I get heads and move to E1, and with probability 1/2 I get tails and stay at E0. So E0 = 1 + 1/2 E1 + 1/2 E0. For E1, after one flip, with probability 1/2 I finish, and with probability 1/2 I go back to E0. So E1 = 1 + 1/2(0) + 1/2 E0 = 1 + 1/2 E0. Then E0 - 1/2 E0 = 1 + 1/2 E1, so 1/2 E0 = 1 + 1/2 E1, hence E0 = 2 + E1. Substitute E1 = 1 + 1/2 E0, so E0 = 2 + 1 + 1/2 E0. Then 1/2 E0 = 3, so E0 = 6.

Correct, and your structure was strong. Interview-level feedback: you should tighten the verbal transitions. In a prop setting, the interviewer wants to hear the state definitions before the algebra, then a crisp solve. Try this style: - Define states in one sentence - Write the recurrence immediately - Solve in two lines - State the answer with a confidence check Next one is faster and more ambiguous: A trader says there is a 60 percent chance of rain today. You independently ask two forecasters. Each forecaster is correct with probability 80 percent and wrong otherwise. One says rain, the other says no rain. What is your updated probability of rain? No calculator. I want your setup first.

I would use Bayes' rule and compare two cases: rain versus no rain. If it rains, the probability of getting one rain and one no rain from the two forecasters is 2 times 0.8 times 0.2, since either forecaster could be the one who is correct or wrong. So that is 0.32. If it does not rain, the same mismatch pattern also has probability 0.32. Then I would combine with priors: prior rain 0.6 times 0.32, prior no rain 0.4 times 0.32. That seems to cancel, which suggests 60 percent again.

Nice catch on the symmetry, and your conclusion is right. Because both forecasters have the same accuracy and the observation is one vote each way, the evidence is uninformative after conditioning on the symmetric setup. So the posterior stays at 60 percent. One improvement: say explicitly why the 2 times 0.8 times 0.2 term appears, and note that it is identical under both hypotheses. That makes the cancellation feel intentional, not accidental. Last one, more prop-trading style: You have 100 coins. 99 are fair, and 1 is double-headed. You pick one coin at random and flip it 10 times, getting 10 heads. What is the posterior probability you chose the double-headed coin? Give me a fast approximation and explain whether the answer is near 1, near 0, or in the middle.

I would compare likelihoods. If the coin is double-headed, probability of 10 heads is 1. If the coin is fair, probability of 10 heads is (1/2)^10 = 1/1024. Prior on double-headed coin is 1/100, and prior on fair coin is 99/100. So posterior is proportional to 1/100 versus 99/100 times 1/1024. That means the double-headed coin is favored by about 1024 to 99, which is roughly 10.4 to 1. So posterior is about 91 percent. The answer is near 1, but not certain.

Good. That is exactly the kind of rapid reasoning a prop interviewer likes. Your estimate is correct and your framing is strong. The key interview win here is that you did not overcompute. You compared likelihoods, used the prior, and made a clean mental approximation. Post-session evaluation: - Probability setup: strong - Bayesian intuition: strong - Speed and approximation: strong - Verbal structure under pressure: good, but can be sharper To improve further, practice answering in this sequence: 1. State the model 2. Compare the hypotheses 3. Do the mental math 4. Give a confidence range, not just a point estimate For your next round, I would drill conditional probability, Markov states, and estimation questions with a stopwatch.