Problem 2: A bowl has two balls in it, and each ball is either red or blue. A ball is removed from the bowl at random, and replaced by another ball. The color of the replacement ball is equally likely to be red or blue. Xn is the number of blue balls in the bowl after the nth replacement.

1. a)Find the transition probability matrix.
2. b)Find the probability that the bowl will have no blue balls in it after two replacements,
3. given that it has no blue balls now.
4. c)Find all 2-step and 3-step transition probabilities.
5. d)Suppose that we are given that the number of blue balls in the bowl is 0 at the start of the
6. process. Find the distribution of the number of blue balls in the bowl after the 3rd replacement.