1. The problem statement, all variables and given/known data An urn contains 3 red and 7 black balls. A and B withdraw balls consecutively until a red ball is selected. Find the probability that A selects the red ball. (A draws the first ball.) 3. The attempt at a solution A selects first => he will win with prob 3/10 B selects second => prob that he gets red is conditional on what colour A took. P(B got red) = P(B got red| A got red)P(A got red) + P(B got red| A not got red)P(A not red) = (2/9)(3/10) + (3/9)(7/10) = 3/10. This seems nonintuitive - it seems the prob of B getting red is independent of what A took. Can someone explain this? Where to go from here?