Compute expected counters after color elimination
Company: Optiver
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
A bag contains 10 red, 10 yellow, and 10 blue counters. Repeatedly draw one counter uniformly at random without replacement (remove it from the bag) until the bag contains counters of only two colors. At that stopping time, what is the expected number of counters remaining in the bag?
Quick Answer: This question evaluates understanding of discrete probability, expected value, and stopping-time concepts in finite sampling without replacement, emphasizing combinatorial reasoning about random draws from a multicolored urn.