Chapter 9.2, Problem 45E

A red urn contains $2$ red marbles and $3$ blue marbles, and a blue urn contains $1$ red marble and $4$ blue marbles. A marble is selected from an urn, the color is noted, and the marble is returned to the urn from which it was drawn. The next marble is drawn from the urn whose color is the same as the marble just drawn. This is a Markov process with two states: draw from the red urn or draw from the blue urn.

(A) Draw a transition diagram for this process.

(B) Write the transition matrix.

(C) Find the stationary matrix and describe the long-run behavior of this process.