Past exam of the mathematics course of the University of Cambridge / 2018 / ib / Paper 3 / 9H / ii

The three year states are transient states: from each there is positive probability of entering an absorbing state, and repeated trials make eventual departure certain because $q<1$. The singleton classes $\{L\}$ and $\{G\}$ are closed absorbing states, hence recurrent. Thus the chain has two closed recurrent classes and three transient singleton classes.