Quant Finance
13 probability questions of the kind asked in quant finance interviews. Each carries a model answer, the concepts a complete response must hit, and graded feedback on your own attempt.
A basic mental-maths screen that tests whether a candidate separates probability from payoff.
You pay $3 to play a game. A fair six-sided die is rolled: you receive $12 on a 6 and nothing otherwise. Should you play once? What would change if you could play 1,000 independent times?
A basic prop-trading exercise tests whether candidates translate probabilities into a price and a trading decision.
A contract pays $100 if a coin lands heads and $0 if it lands tails. You believe heads has a 55% probability. What is the fair value? Would you buy at $54, and would you sell at $56?
Asked to see whether you can explain a counterintuitive result clearly under pressure.
Three doors: one hides a car, two hide goats. You pick door 1. The host. Who knows what's behind each door. Opens door 3 revealing a goat, then offers you the chance to switch to door 2. Should you switch? Explain why in…
Fermi estimation is a standard prop trading round. You have sixty seconds.
How many tennis balls fit in a Boeing 747? You have one minute.
Tests recursive reasoning. A staple at trading firms.
You roll a fair six-sided die. You may either take the value shown in dollars, or re-roll. You get at most two rolls total. What is the expected value of the game if you play optimally? Then: what if you had unlimited…
A Bayesian question testing whether you anchor on the prior or the evidence.
A test for a condition affecting 1 in 1,000 people is 99% accurate. 99% true positive rate and 99% true negative rate. Someone tests positive. What is the probability they have the condition?
Tests whether you can approximate rather than recall.
In a room of 23 people, what is the probability at least two share a birthday? Explain your reasoning and why the answer surprises people.
A classic Bayesian warm-up at quant trading firms.
You have two coins. One is fair; the other lands heads 75% of the time. You pick one at random and flip it 3 times, getting heads every time. What is the probability you picked the biased coin?
The interactive trading game used at every prop firm.
I have a bag with 10 balls, each numbered 1 to 10. I draw three and the contract settles on their sum. Make me a market. Then I show you that one of the balls drawn is a 10, what's your new market?
The signature exercise at proprietary trading firms.
Make me a market on the sum of the digits of a randomly chosen phone number in the room. Then I'll trade against you. Explain how you'd think through the whole exercise.
Tests whether you reason about why a bet is being offered, not just its expected value.
I offer you a bet: I roll a fair die, and if it comes up 6 I pay you $10; otherwise you pay me $1. Do you take it? How much would you pay for the right to play 100 times?
A recurring structure in quant interviews. Set up the recursion, don't simulate.
You start at position 0. Each step you move +1 with probability 0.5 and −1 with probability 0.5. What is the expected number of steps to first reach +3? Then: what changes if the walk is bounded below at −1 (you cannot…
Trading firms use this to test whether you understand compounding and ruin.
You have an edge: a bet that pays 2:1 and wins 40% of the time. What fraction of your capital should you bet, and why not more?
Write your answer, get it graded on technical accuracy, completeness and communication, and see exactly which mechanic you missed.
Firm names indicate where a question type is commonly reported in interviews. They are not sourced from, endorsed by, or affiliated with the firms named.