The white ball that is drawn first is not equally likely to be B or A. Given that the first ball is white, there is a 2/3 chance that it is A. (draw a tree diagram to check this)
P(second ball is white) = P(both were white|at least one is white) = P(both were white)
You are given this probability as 50%.
im not sure, which is actually pretty alarming but never mind.