{"status": "success", "data": {"description_md": "Consider the open interval from $0$ to $5$ on a number line. Two points distinct points $x$ and $y$ are chosen at random on the open interval with no restrictions. These points divide the number line into $3$ regions $a$, $b$, and $c$ from left to right. The probability that $a<2b<c$ can be expressed as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime, positive integers. Compute the value of $m+n$.", "description_html": "<p>Consider the open interval from <span class=\"katex--inline\">0</span> to <span class=\"katex--inline\">5</span> on a number line. Two points distinct points <span class=\"katex--inline\">x</span> and <span class=\"katex--inline\">y</span> are chosen at random on the open interval with no restrictions. These points divide the number line into <span class=\"katex--inline\">3</span> regions <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span>, and <span class=\"katex--inline\">c</span> from left to right. The probability that <span class=\"katex--inline\">a&lt;2b&lt;c</span> can be expressed 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 the value of <span class=\"katex--inline\">m+n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "TxO Math Bowl 2024 - Team Contest - Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024team-p09", "prev": "/problem/txo2024team-p07"}}