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 t + 1 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 k1N 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.