I have the following question in my assignment but I do not know how to proof:

Bunny rabbit has three dens A, B and C. It likes A better than B and C. If it's in B or C on

any night, it will always take chance 0.9 to go to A and chance 0.1 to go to the other den for the

following night. Once it reaches A, it will stay there for two nights and the third night will be in

B or C with equal chance 0.5. Let Xn be the stats Bunny is in for night n.

**Question:**

If the state space of the {Xn} is given by {First night at den A; Second night at den A; den B; den C}

then is {Xn} a MC?

Thanks.