In this experiment there are i balls in Urn I, and remaining 2n-i balls in Urn II. Then at any instance, the probability of selecting a ball from Urn I and placing it in Urn II is i/2n, and the other way of placing a ball from Urn II to Urn I is (2n-i)/2n. At each instant we let the number i of balls in the Urn I to be the state of the system. Thus, the state space is S = { 0, 1, 2, ..., 2n }. Then we can pass from state i only to either of the states i-1 or i+1.
Here, S = {0, 1, ..., 2n}.