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

1. 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?
2. 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.