CEMC Cayley, 2005

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer Canada

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 $B$ ?

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

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