A box contains three white and three black balls. A randomly chosen ball is removed from the box. If the chosen ball is white, a black ball is added to the box. If the chosen ball is black, a white ball is added to box. (The chosen ball isn't put back in the box.) This procedure is repeated two more times.
(a) Are the colors of first, second, and third randomly chosen balls independent? If not, explain why.
(b) What is the probability that at the end the bag haves at least one white ball and at least one black ball?
(c) Determine the probability that the second randomly selected ball is white?