Originally Posted by

**qmech** Since the player went to the 3rd stage, he must have had a white ball on the 3rd draw and 2 balls of the same color on the 1st 2 draws.

What was the probability he had 2 greens on the 1st 2 draws?

Probability 1st ball is green is 3/5.

Probability 2nd ball is green is 2/4.

Total prob = 3/10.

What was the probability he had 2 blues on the 1st 2 draws?

Probability 1st ball is blue is 2/5.

Probability 2nd ball is blue is 1/4.

Total prob = 1/10.

We know we are in one of these 2 situations. The relative probability of blue to green is 1:3, so the probability we had taken 2 blues is 1:4.