An urn contains six balls, of which three are red and three are green. Two balls are selected from the urn. If one ball is red and the other is green, then the selected balls are discarded and two blue balls are returned to the urn. Otherwise, the selected balls are returned to the urn (This is an elementary model of a chemical reaction in which red and green atoms combine to form a blue molecule). Assume that the process stops once there are no red balls in the urn. Model this process as a Markov chain. Give the transition probability matrix