AMC 12 2020a Problem 11

A frog sitting at the point $(1, 2)$ begins a sequence of jumps, where each jump is parallel to one of the coordinate axes and has length $1$, and the direction of each jump (up, down, right, or left) is chosen independently at random. The sequence ends when the frog reaches a side of the square with vertices $(0,0), (0,4), (4,4),$ and $(4,0)$. What is the probability that the sequence of jumps ends on a vertical side of the square$?$

$\textbf{(A) } \frac{1}{2} \textbf{(B) } \frac{5}{8} \textbf{(C) } \frac{2}{3} \textbf{(D) } \frac{3}{4} \textbf{(E) } \frac{7}{8}$