Markov Chains & Long-Run Behavior · Easy problem

A three-state chain has transition matrix $M = \begin{pmatrix} 1/2 & 0 & 1/3 \\ 1/4 & 1/2 & 1/3 \\ 1/4 & 1/2 & 1/3 \end{pmatrix}$ ($M_{ij}$ is the probability of moving to state $i$ from state $j$) and starting distribution $\mathbf x_0 = \begin{pmatrix} 1/2 \\ 0 \\ 1/2 \end{pmatrix}$. What is the probability of being in state 2 after one step? Express your answer as a common fraction.