Compute two conditional probability scenarios
Company: Capital One
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: HR Screen
Answer both parts, showing formulas and a final numeric value. A) You have a box with 3 fair coins and 2 double‑headed coins. You pick one coin uniformly at random, flip it three times, and observe H,H,H. What is P(coin is double‑headed | 3 heads observed)? B) An urn contains 5 red, 4 blue, and 3 green balls. You draw 3 balls without replacement. What is the probability that exactly two distinct colors appear and at least one ball is red?
Quick Answer: This question evaluates a candidate's understanding of conditional probability, Bayesian reasoning for posterior inference, and combinatorial counting in finite-sample probabilities.
