Compute odds under time pressure
Company: Optiver
Role: Quantitative Trader
Category: Statistics & Math
Difficulty: medium
Interview Round: Online Assessment
Answer a timed probability question: An urn contains r red, b blue, and g green balls (r,b,g ≥ 0, r+b+g ≥
3). You draw 3 balls without replacement. Compute the probability that you draw at least two reds within 90 seconds, and present a fast mental-math method that scales to general parameters. Extend your solution to (i) drawing with replacement, (ii) conditional probability given that the first ball was green, and (iii) odds ratio form suitable for quick estimation.
Overview: This question evaluates probabilistic reasoning and combinatorial calculation skills, including conditional probability, distributional thinking and the ability to convert probabilities into odds.