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 +∞