Solution
= Solution
Reading the directed edges with positive transition probability, the communicating classes are
$$
\boxed{\{3\},\qquad\{4\},\qquad\{1,2,5,6\}}.
$$
State $3$ can move to $2$ or $4$, and state $4$ can move to $2$ or $5$, so their singleton classes are not closed. Every transition from $1,2,5,$ or $6$ remains within $\{1,2,5,6\}$, so
$$
\boxed{\{1,2,5,6\}\text{ is the unique closed class}}.
$$