An urn initially contains two black balls and two white balls. The following experiment is repeated indefinitely: A ball is drawn from the urn; with probability a, the color of the ball is changed to the other color and is then put back in the urn, otherwise it is put back without change.
Let Xn be the number of black balls in the urn after n draws from the urn.

(a) Is Xn a Markov process? If so, find the appropriate transition probabilities.
(b) Do the transition probabilities depend on n?
(c) Repeat part a if a = 1. What changes?
(d) Repeat parts a and c if the urn contains K black balls and K white balls.