Consider a total of 3 red balls and 3 blue balls. There are two urns labeled A and B, each containing 3 balls. An experiment consists of picking one ball at random from each urn and interchanging the balls. This experiment is repeated independently again and again. Let Xn be the number of red balls in urn A after n repetitions of the experiment. 1. (20pt) Write down the transition matrix of Markov chain {Xn, n 20 2. (20pt) Suppose that all the 3 red balls are in urn A at the beginning, i. e., X0-3. Compute the expected number of experiments we need to find that, for the first time, all the 3 red balls are in urn B.