{"status": "success", "data": {"description_md": "Let $P$ be a point chosen uniformly at random in the interior of the unit square with vertices at $(0,0), (1,0), (1,1)$, and $(0,1)$. The probability that the slope of the line determined by $P$ and the point $\\left(\\frac58, \\frac38 \\right)$ is greater than $\\frac12$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

Let P be a point chosen uniformly at random in the interior of the unit square with vertices at (0,0), (1,0), (1,1), and (0,1). The probability that the slope of the line determined by P and the point \\left(\\frac58, \\frac38 \\right) is greater than \\frac12 can be written as \\frac{m}{n}, where m and n are relatively prime positive integers. Find m+n.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2020 AIME II Problem 2", "can_next": true, "can_prev": true, "nxt": "/problem/20_aime_II_p03", "prev": "/problem/20_aime_II_p01"}}