There are four opaque bags, each of which contain three marbles. One has three white marbles, one has two black marbles and a white marble, one has two white marbles and a black marble, and the last contains three black marbles.

a) A bag is selected randomly and a marble is randomly selected from that bag. It is black. Another marble is selected randomly from the same bag. What is the probability that it is black?

b) A bag is selected randomly and TWO marbles are randomly selected from that bag. BOTH are black. What is the probability that the one remaining marble in that bag is black?

c) One marble is removed from three different bags. The results are B, W, W. A second marble is removed from the same bag from which the black marble was removed. What is the probability it is black?

d) One marble is removed from three different bags. The results are B, W, W. Now a marble is removed from fourth bag, which still contains three marbles. What is the probability it is black?