Probability quant interview questions

Probability questions are the backbone of quant trading and quant research interviews. Interviewers use them to see how quickly you can model an unfamiliar situation, choose the right sample space and avoid double counting under time pressure. Expect conditional probability and Bayes' rule, independence traps, geometric probability, symmetry arguments, coin and dice games, and Markov chain style problems where you set up states and solve a small system of equations. The problems below start with short warm-ups and build toward multi-step questions with interviewer follow-ups, the kind asked in first rounds at trading firms and hedge funds. Each free problem includes hints and a worked, step-by-step solution, so you can learn the reasoning pattern rather than memorising an answer, then practise it interactively.