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.

(b) Let Yn denote the number of red balls in the urn immediately before the nth ball is selected. Is {Ym n 2 1} a Markov chain? Ifso, 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