2003 Fermat Problem 11

In the diagram, it is only possible to travel along an edge in the direction indicated by the arrow. Hazel studied the figure, and determined all the possible routes from A to B. She selected one of these routes at random. What is the probability that she selected a route which passes through X?

\textbf{(A)}\ \frac{8}{11}\quad \textbf{(B)}\ \frac{3}{11}\quad \textbf{(C)}\ 1\quad \textbf{(D)}\ \frac{9}{11}\quad \textbf{(E)}\ \frac{6}{11}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.