4 blue balls and 4 green balls are distributed evenly into two urns (labelled as Urn A and Urn B) such that each urn contains four balls. At each step, we draw one ball from each urn and exchange them. Let Xn be the number of blue balls in Urn A at time n. Then, (Xn)n is a Markov chain on state space {0, 1, 2, 3, 4}.

(a) Give the transition probabilities of the Markov chain.

(b) Compute P(X₂ = 2|X₀ = 2).

(c) Obtain the stationary distribution.