Compute probability with colored balls draws
Company: Virtu Financial
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
##### Question
You have 5 red, 5 blue, and 5 green balls in a bag. You draw balls one at a time without replacement, but each time you draw a green ball you return it to the bag. You keep any red or blue balls drawn. When you have three balls in hand, what is the probability that at least two of them are red? Follow-up: If instead the bag initially contains 10 red balls (with the same 5 blue and 5 green), what is the probability that at least two of the three balls held are red?
Quick Answer: This question evaluates understanding of probability theory, conditional probability, and probabilistic modeling under nonstandard draw rules (replacement of a specific color), emphasizing counting and likelihood computation.