{"status": "success", "data": {"description_md": "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 $4$.\n\nJosh 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 $m + n$.\n\n$(\\textbf{A})\\;76\\quad(\\textbf{B})\\;77\\quad(\\textbf{C})\\;78\\quad(\\textbf{D})\\;79\\quad(\\textbf{E})\\;80$", "description_html": "<p>Josh is playing on monkey bars, starting on bar number <span class=\"katex--inline\">1</span>. Josh can either swing <span class=\"katex--inline\">1</span> bar over, or swing <span class=\"katex--inline\">2</span> bars and skip one. For example, Josh can go from bar <span class=\"katex--inline\">1</span> to bar <span class=\"katex--inline\">3</span>, and then to bar <span class=\"katex--inline\">4</span>.</p>&#10;<p>Josh has a <span class=\"katex--inline\">\\frac{3}{4}</span> chance of swinging <span class=\"katex--inline\">1</span> bar, and a <span class=\"katex--inline\">\\frac{1}{4}</span> chance to swing <span class=\"katex--inline\">2</span> bars. If the probability of Josh skipping bar <span class=\"katex--inline\">4</span> can be represented as <span class=\"katex--inline\">\\frac{m}{n}</span> where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime positive integers, compute <span class=\"katex--inline\">m + n</span>.</p>&#10;<p><span class=\"katex--inline\">(\\textbf{A})\\;76\\quad(\\textbf{B})\\;77\\quad(\\textbf{C})\\;78\\quad(\\textbf{D})\\;79\\quad(\\textbf{E})\\;80</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Mock AMC 8 #1 - Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/amc8mock1-p24", "prev": "/problem/amc8mock1-p22"}}