3.3.8 Two urns A and B contain a total of N balls. Assume that at time t, there were exactly k balls in A. At time tC1, an urn is selected at random in proportion to its contents (i.e., A is chosen with probability k=N and B is chosen with probability .N ????k/=N). Then, a ball is selected from A with probability p or from B with probability q and placed in the previously chosen urn. Determine the transition matrix for this Markov chain.