Consider a sample of size 3 drawn in the following manner. One starts with an urn containing 5 white and 7 red balls. At each trial a ball is drawn and its color is noted. The ball drawn is then returned to the urn, together with an additional ball of the same color. Find the probability that the sample will contain exactly (i) 0 white balls, (ii) 1 white ball, (iii) 3 white balls.