2005 Cayley Problem 18

Harry the Hamster is put in a maze, and he starts at point S. The paths are such that Harry can move forward only in the direction of the arrows. At any junction, he is equally likely to choose any of the forward paths. What is the probability that Harry ends up at B?

\textbf{(A)}\ \frac{2}{3}\quad \textbf{(B)}\ \frac{13}{18}\quad \textbf{(C)}\ \frac{11}{18}\quad \textbf{(D)}\ \frac{1}{3}\quad \textbf{(E)}\ \frac{1}{4}

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

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