Compute probability in urn with green returns
Company: Virtu Financial
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
An urn contains 5 red, 5 blue, and 5 green balls. You repeatedly draw one ball uniformly at random. If the ball is green, immediately return it to the urn and continue; if it is red or blue, keep it. Stop once you are holding three balls (i.e., three non-green balls).
1) What is the probability that at least two of the three held balls are red?
2) Now suppose the urn instead has 10 red, 5 blue, and 5 green balls (same process). First give an intuitive estimate, then compute the exact probability that at least two of the three held balls are red.
Quick Answer: This question evaluates understanding of probability theory and combinatorics, focusing on conditional probabilities, stopping-time processes, and how replacement of certain outcomes affects sampling distributions.