3.3.9 Suppose that two urns A and B contain a total of N balls. Assume that at time t, there are exactly k balls in A. At time tC1, a ball and an urn are chosen with probability depending on the contents of the urn (i.e., a ball is chosen from A with probability k=N or from B with probability .N ????k/=N). Then, the ball is placed into one of the urns, where urn A is chosen with probability k=N or urn B is chosen with probability .N ????k/=N. Determine the transition matrix of the Markov chain with states represented by the contents of A.