An urn initially contains 2 balls, one of which is red and the other blue. at each stage a ball is randomly selected. if the selected ball is red, then it is replaced with a red ball with probability .7 or with a blue ball with probability .3; if the selected ball is blue, then it is equally likely to be replaced by either a red or blue ball.

a. let xn equal 1 if the nth ball selected is red, and let it equal 0 other- wise. is {xn , n ≥ 1} a markov chain? if so, give its transition probability matrix.
b. let yn denote the number of red balls in the urn immediately before the nth ball is selected. is {yn , n ≥ 1} a markov chain? if so, give its transition probability matrix.
c. find the probability that the second ball selected is red.
d. find the probability that the fourth ball selected is red.