What does the notation $P_{\overline{MM}}(t)$ mean in this context?

Question

The notation $P_{\overline{MM}}(t)$ is used in part (iii) of the following question:

I'm unsure of exactly what this notation represents. My guess would be that it represents the probability that a person who starts in the state $M$ at time $0$, is in the state $M$ at time $t$. Is this correct?

Answer 1

The notation $P_{\overline{MM}}(t)$ denotes the probability that the process remains in the state $M$ for $t$ periods, without ever leaving that state, given that it starts in state $M$ at time $0$.