Suppose we have two boxes labeled 1 and 2 and 3 balls labeled 1, 2, and 3. Initially, some of the balls are in box 1 and the remainder in box 2. An integer is selected at random from 1, 2 , 3 and the ball labeled by that integer is removed from its box. We now select at random one of the two boxes and put the removed ball into this box. The procedure is repeated indefinitely and the selection being made independently. Let Xn denote the number of balls in box 1 after the nth trial. Find the transition probability matrix for this Markov chain.