Consider the pair of Ehrenfest urns studied in Section 10.2, Exercise 10. Suppose that urn A is now empty. How many steps on average will be needed until urn A is again empty?

Data From Section 10.2 Exercise 10

Consider a pair of Ehrenfest urns with a total of 5 molecules divided between them.
a. Find the transition matrix for the Markov chain that models the number of molecules in urn A, and show that this matrix is not regular.
b. Assuming that the steady-state vector may be interpreted as occupation times for this Markov chain, in what state will this chain spend the most steps?