Consider a sample of size 3 drawn in the following manner: We start with an urn containing 5 white and 7 red balls. At each stage, a ball is drawn and its color is noted. The ball is then returned to the urn, along with an additional ball of the same color. Find the probability that the sample will contain exactly
(a) 0 white balls;
(b) 1 white ball;
(c) 3 white balls;
(d) 2 white balls.