There are six balls (three black and three white) that are distributed in two bags, such that each bag contains three balls. At each step, you randomly draw one ball from each bag. Then place the ball drawn from the first bag to the second, and place the ball drawn from the second bag to the first. Assume that we are interested in the stochastic process that keeps track of the distribution of the balls of different colors in the bags.

a)Briefly explain why this system can be modeled as a markov chain.

b)Define the states of the markov chain.

c)Provide the state transition matrix. Show all your calculations.

d)Is this markov chain ergodic? Explain why/why not.