I have a Markov chain with three states, X, Y and Z, and the following transition matrix;
$$ P =\pmatrix{0.5 & 0.5 & 0 \\ 0.4 & 0.4 & 0.2 \\ 0 & 0.5 & 0.5 \\}$$
Now, what I need is to compute the probability of being in states Y or Z next "turn" given we're currently either in state Y or Z.
So, if we were in state Y, the probability of being in state Y or Z next turn would be 0.6. If we were in state Z, the probability of being in state Y or Z next turn would be 1.
The problem I'm having is what to do with both these probabilities to get my final answer.