Quant Probability and Statistics Orals

Quant finance rounds include oral probability and statistics: nested radicals, couple-selection probability, dice expected value, first-heads coin-toss probability, and tests for whether a sample follows a binomial distribution. Requirements Be ready to solve and explain several short oral questions: Evaluate sqrt(2 + sqrt(2 + sqrt(...))) as an infinite expression. From 5 couples, choose 4 people uniformly; compute the probability that the selected group contains exactly 2 complete couples. Compute the expected value of a dice game and decide how much you should pay to play. In a coin-toss game where the first person to throw heads wins, compute the first player's win probability. Choose an appropriate test to evaluate whether a sample distribution follows a binomial distribution. Show setup and assumptions, not just final numbers. Notes Infinite radical setup: let x = sqrt(2 + x), solve x^2 = 2 + x, then keep the positive root. Couple-selection problem: the favorable outcome is selecting all members of exactly two couples; compare against all ways to choose 4 people from 10. For distribution testing, name the hypothesis, expected bin counts, sample-size requirements, and a goodness-of-fit test such as chi-square when assumptions are met. Dice EV and coin-toss questions are graded on clean probability-space setup and expected-value reasoning. Preparation Drill five-minute oral solutions for EV, geometric-series probability, and simple combinatorics. Practice stating assumptions before calculating: fair die / coin, independent trials, uniform selection, and replacement rules. Review chi-square goodness-of-fit prerequisites and how binomial parameters are estimated or specified.