The graph below shows a small maze, in the form of a network of directed routes. The vertices A to F show junctions in the maze and the edges show the possible paths available from one vertex to another. A mouse is placed at vertex A and left to wander the maze freely. The routes shown by dashed lines indicate paths sprinkled with sugar. When the mouse reaches any junction, she rests for a constant time before continuing.

Note: Allow the transposed matrix. Award $\boldsymbol{M1}$ for a $6 \times 6$ matrix with all values between 0 and 1 , and all columns (or rows if transposed) adding up to 1, award $\boldsymbol{A1}$ for one correct row (or column if transposed) and $\boldsymbol{A1}$ for all rows (or columns if transposed) correct.

attempting to raise the transition matrix to a large power steady state vector is $\left(\begin{array}{c}(0.157) \\ (0.0868) \\ (0.256) \\ (0.241) \\ (0.0868) \\ 0.173\end{array}\right)$ so percentage of time spent at vertex F is $17.3\%$

Note: Accept $17.2\%$.

the model assumes instantaneous travel from junction to junction,

OR

the mouse may eat the sugar over time R1 and hence the probabilities would change R1 Note: Accept any other sensible answer.