Three hats each contain ten coins. Hat 1 contains two gold coins, five silver coins and three copper coins. Hat 2 contains four gold coins and six silver coins. Hat 3 contains three gold coins and seven copper coins. We randomly select one coin from each hat.

(a) The outcome of interest is the color of each of the three selected coins. List the complete sample space of outcomes and calculate the probability of each.

(b) Let X be the number of gold coins selected. Find the probability distribution of X.