Consider the following random process. initially, there are n red balls in an urn. at each step, a ball chosen uniformly at random from the urn is removed, and then a blue ball is placed into the urn. (note that after each step, there are n balls in the urn.) all random choices in this process are made independently. after n steps, what is the expected fraction of balls in the urn that are red? in other words, if xt denotes the number of red balls in the urn after t steps, what is e[xn/n]?
for this problem, regard n as a large number tending to +[infinity]