Alice and Bob vote in each parliamentary election. If, in a certain election, Alice and Bob vote for the same party, they vote for it again in the next election. If they vote for different parties, next each of them switches their opinion independently with probability 1/4 .
1. Devise a Markov model to describe their votes in the n-th election, under the simplifying assumptions that they are immortal, the parliamentary system in the UK is stable and there are only two parties (C and L).
2. Draw the transition graph and write down the transition matrix (note that you need to number the states!)
3. Assume that in the n-th election Alice voted C and Bob voted L. What is the (conditional) probability that in the n + 2-nd election Alice will vote L and Bob will vote C?
4. Assume that in the n-th election Alice and Bob both voted L. What is the (conditional) probability that in the n − 1-st election Alice voted C?
