Question 3) (25 points) A game involves four balls and two urns (i.e., Urn 1 and Urn 2). In each round, you select one of these balls randomly, and change the urn of that ball. (a) (9 points) Describe the probabilistic evolution of this process as a Markov chain, define the states and write down a one-step transition probability matrix. (b) (10 points) Suppose initially that balls are evenly distributed between the urns. What is the probability that after two rounds of ball selection, there are three balls in Urn 1 and one ball in Urn 2? (c) (6 points) Suppose now that ball selection likelihoods change in the following sense: there is a 60% chance a ball will be selected from Urn 1 , and 40% chance a ball is selected from Urn 2 as long as there is at least one ball in both urns. How does the onestep transition probability matrix change in this case