Mock AMC 8 #1 - Problem 23

Josh is playing on monkey bars, starting on bar number 1. Josh can either swing 1 bar over, or swing 2 bars and skip one. For example, Josh can go from bar 1 to bar 3, and then to bar 4.

Josh has a \frac{3}{4} chance of swinging 1 bar, and a \frac{1}{4} chance to swing 2 bars. If the probability of Josh skipping bar 4 can be represented as \frac{m}{n} where m and n are relatively prime positive integers, compute m + n.

(\textbf{A})\;76\quad(\textbf{B})\;77\quad(\textbf{C})\;78\quad(\textbf{D})\;79\quad(\textbf{E})\;80