{"status": "success", "data": {"description_md": "Let there be $6$ magical fish that  in a tank, $3$ of them are male, and $3$ of them are female. A breeder arbitrarily puts the $6$ fish into $3$ fish bowls such that each bowl houses $2$ fish. If the two fish in each bowl are of opposite sex, they instantly fall in love (W Rizz) and immediately give birth to a baby fish. Otherwise, nothing will happen. If the expected value of the total number of fish, after they are placed into their bowls, allowed to fall in love, and give birth, can be expressed as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers, find $m + n$.", "description_html": "<p>Let there be <span class=\"katex--inline\">6</span> magical fish that  in a tank, <span class=\"katex--inline\">3</span> of them are male, and <span class=\"katex--inline\">3</span> of them are female. A breeder arbitrarily puts the <span class=\"katex--inline\">6</span> fish into <span class=\"katex--inline\">3</span> fish bowls such that each bowl houses <span class=\"katex--inline\">2</span> fish. If the two fish in each bowl are of opposite sex, they instantly fall in love (W Rizz) and immediately give birth to a baby fish. Otherwise, nothing will happen. If the expected value of the total number of fish, after they are placed into their bowls, allowed to fall in love, and give birth, 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, find <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 - Guts Contest - Set 3 Problem 3", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}