An urn contains m red and n white balls.
(a) We draw two balls randomly and simultaneously. Describe the sample space and calculate the probability that the selected balls are of different color, by using two approaches: a counting approach based on the discrete uniform law, and a sequential approach based on the multiplication rule.
(b) We roll a fair 3-sided die whose faces are labeled 1 ,2,3, and if k comes up. we remove k balls from the urn at random and put them aside. Describe the sample space and calculate the probability that all of the balls drawn are red. using a divide-and-conquer approach and the total probability theorem.