2020 AMC 12A 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} \qquad \textbf{(B) } \frac{5}{8} \qquad \textbf{(C) } \frac{2}{3} \qquad \textbf{(D) } \frac{3}{4} \qquad \textbf{(E) } \frac{7}{8}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.