Consider the Bernoulli-Laplace diffusion model studied in Section 10.1, Exercise 34.
a. Let k = 5 and show that the transition matrix for the Markov chain that models the number of type I molecules in urn A is regular.
b. Let k = 5. In what state will this chain spend the most steps, and what fraction of the steps will the chain spend at this state?

Data From Section 10.1 Exercise 34

Another model for diffusion is called the Bernoulli-Laplace model. Two urns (urn A and urn B) contain a total of 2k molecules. In this case, k of the molecules are of one type (called type I molecules) and k are of another type (type II molecules). In addition, k molecules must be in each urn at all times. At each time step, a pair of molecules is selected, one from urn A and one from urn B, and these molecules change urns. Let the Markov chain model the number of type I molecules in urn A (which is also the number of type II molecules in urn B).