At each stage, a ball is randomly selected from the urn. A coin having probability 0.6 of landing heads is then flipped. If heads appears, the selected ball is replaced by a white ball and returned to the urn. If tails appears, the selected ball is replaced by a black ball and returned to the urn. Let Xn denote the number of white balls in the urn after the nth stage. Required:
Find the non-zero transition probabilities.