{"status": "success", "data": {"description_md": "Geeks is playing a game of Entry Point with Victor, a fun multiplayer FPS game in Roblox. They are currently working together to complete a mission. If Geeks is talking about Bedwars, he gets distracted.\n\nThis leads Geeks to have a $\\frac{3}{4}$ chance of losing the game. If Geeks is not talking about Bedwars, and is focused, he has a $\\frac{1}{8}$ chance of losing the game. Victor has a $\\frac{1}{4}$ chance of talking about Bedwars and inadvertently distracting Geeks.\n\nIn addition, Victor has a $\\frac{1}{16}$ chance of losing the game. (Geeks and Victor are playing the same game, so if one of them lose, they both lose. In addition, the only 2 possible results of the game are either a win or a loss).\n\nLet $\\frac{m}{n}$ denote the probability of Geeks and Victor winning the game where $\\gcd(m, n) = 1$ and $m, n \\in \\mathbb{Z}^+$. Compute $m + n$.", "description_html": "<p>Geeks is playing a game of Entry Point with Victor, a fun multiplayer FPS game in Roblox. They are currently working together to complete a mission. If Geeks is talking about Bedwars, he gets distracted.</p>&#10;<p>This leads Geeks to have a <span class=\"katex--inline\">\\frac{3}{4}</span> chance of losing the game. If Geeks is not talking about Bedwars, and is focused, he has a <span class=\"katex--inline\">\\frac{1}{8}</span> chance of losing the game. Victor has a <span class=\"katex--inline\">\\frac{1}{4}</span> chance of talking about Bedwars and inadvertently distracting Geeks.</p>&#10;<p>In addition, Victor has a <span class=\"katex--inline\">\\frac{1}{16}</span> chance of losing the game. (Geeks and Victor are playing the same game, so if one of them lose, they both lose. In addition, the only 2 possible results of the game are either a win or a loss).</p>&#10;<p>Let <span class=\"katex--inline\">\\frac{m}{n}</span> denote the probability of Geeks and Victor winning the game where <span class=\"katex--inline\">\\gcd(m, n) = 1</span> and <span class=\"katex--inline\">m, n \\in \\mathbb{Z}^+</span>. Compute <span class=\"katex--inline\">m + n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "Christmas Contest - Individual Round - Problem 3", "can_next": true, "can_prev": true, "nxt": "/problem/christmas1_individual-p04", "prev": "/problem/christmas1_individual-p02"}}