Answer¶
Using balance equations, we have
\[
\begin{aligned}
\pi_{1} &= \pi_{1}p_{11} + \pi_{2}p_{21}\newline
\pi_{2} &= \pi_{1}p_{12} + \pi_{2}p_{22}\newline
\pi_{1} + \pi_{2} &= 1
\end{aligned}
\]
Solving, \(\pi_{1} = \frac{2}{7}\) and \(\pi_{2} = \frac{5}{7}\)