Compute probability in urn with green returns

Q: Compute probability in urn with green returns

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.

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Question

Urn Sampling with Replacement for Greens Only

You have an urn with colored balls. You repeatedly draw one ball uniformly at random:

If the ball is green, immediately return it to the urn and continue.
If the ball is red or blue, keep it out of the urn.
Stop once you are holding three balls (i.e., three non-green balls).

This means greens only affect how long it takes, not the colors of the three held balls.

Questions

Case A: The urn contains 5 red, 5 blue, and 5 green balls. What is the probability that at least two of the three held balls are red?
Case B: The urn contains 10 red, 5 blue, and 5 green balls. First give an intuitive estimate, then compute the exact probability that at least two of the three held balls are red.

Compute probability in urn with green returns

Urn Sampling with Replacement for Greens Only

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Compute probability in urn with green returns

Overview

Urn Sampling with Replacement for Greens Only

Questions

Solution

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