Expected Value vs Probability in Quant Interviews
How to tell whether a quant interview question asks for probability, expected value, fair price, or a decision.
Candidates who mix up likelihoods, payoffs, values, and trading choices.
Probability answers likelihood
A probability question asks how likely an event is. The answer must be between zero and one, or between 0 percent and 100 percent. Sample spaces, complements, and conditioning usually drive the solution.
Expected value answers average payoff
An expected value question asks what an uncertain payoff is worth on average under the model. The answer has payoff units, not probability units. It can be negative, positive, or outside the range of probabilities because it is not a likelihood.
Fair price adds market language
A fair price is often the expected payoff under risk-neutral or simplified assumptions. In interviews, say what assumptions make the price fair and whether variance, constraints, or repeatability would change the trade decision.
Concrete example
For a game paying 10 dollars if a die shows six, the probability of winning is 1/6. The expected payoff is 10/6 dollars. Whether you take the game at a price of 2 dollars depends on expected profit and the risk context.
Decision questions need more
A positive expected value does not automatically settle sizing. Discuss variance, bankroll, limits, and whether the game repeats. Trading interviews reward candidates who separate value from risk management.
Common mistakes
Candidates give an expected value when asked for a probability, or say "take it" after a positive EV without discussing constraints. Start by naming the target before calculating.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.