Compute probability with colored balls draws
Overview
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.
Virtu Financial
Aug 4, 2025, 10:55 AM
Data Scientist
Technical Screen
Statistics & Math
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Probability with Replacement-on-Green Draws
Context
You have a bag with colored balls. You draw balls one at a time. Any time you draw a green ball, you put it back (it does not count toward the balls you hold). Any red or blue ball you draw is kept and removed from the bag. You stop once you are holding 3 balls (i.e., 3 kept balls, all of which are red or blue).
Questions
- The bag starts with 5 red, 5 blue, and 5 green balls. What is the probability that at least two of the three held balls are red?
- Follow-up: If instead the bag starts with 10 red, 5 blue, and 5 green balls, what is the probability that at least two of the three held balls are red?
Solution
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