An urn initially contains one white and one black ball At each stage a ball is drawn and is then replaced in the urn along with another ball of the same color. Let Z, denote the fraction of balls in the urn that are white after the nth replication.

(a) Show that {Zn, n 1} is a martingale.

(b) Show that the probability that the fraction of white balls in the urn is ever as large as 3/4 is at most 2/3.