13. A frog starts a series of jumps from point $(1,2)$, with each jump parallel to one of the coordinate axes and 1 unit in length. It is known that the direction of each jump (up, down, right, or left) is randomly chosen. The frog stops jumping when it reaches the boundary of the square with vertices at $(0,0)$, $(0,4)$, $(4,4)$, and $(4,0)$. What is the probability that the frog stops on a vertical side of the square?
(A) $\frac{1}{2}$
(B) $\frac{5}{8}$
(C) $\frac{2}{3}$
(D) $\frac{3}{4}$
(E) $\frac{7}{8}$
13. B.

If the frogs are on any diagonal, the probability of them landing on a vertical or horizontal line becomes $\frac{1}{2}$. Starting from point $(1,2)$, there is a $\frac{3}{4}$ probability (up, down, or right) of reaching the diagonal on the first jump, and a $\frac{1}{4}$ probability (left) of reaching the vertical side.
Thus, the required probability is $\frac{1}{4}+\frac{3}{4} \times \frac{1}{2}=\frac{5}{8}$.