Two containers are filled with ping-pong balls. The red container has 100 red balls, and the blue container has 100 blue balls. In each step a container is selected; red with probability 1/2 and blue with probability 1/2. Then, a ball is selected from it - all balls in the container are equally likely to be selected - and placed in the other container. If the selected container is empty, no ball is transfered.
Once there are 100 blue balls in the red container and 100 red balls in the blue container, the game stops (and we stay in that state forever).
We decide to model the situation as a Markov chain.
What is the state space S we can use? How large is it?
What is the initial distribution?
What are the transition probabilities between states? Don't write the matrix, it is way too large; just write a general expression for pij, i,j ∈ S.
How many transient states are there?