{"status": "success", "data": {"description_md": "There are $n$ baskets of apples and $m$ baskets of bananas. Each basket has a random number of apples and bananas. The probability of you randomly picking up an apple is $\\frac13$, and the probability of you picking up an apple after picking up a banana is $\\frac{13}{27}$. If the probability of you picking up a banana after picking up an apple can be expressed as $\\frac{a}{b}$, where $a$ and $b$ are relatively prime, positive integers, compute $a+b$.", "description_html": "<p>There are <span class=\"katex--inline\">n</span> baskets of apples and <span class=\"katex--inline\">m</span> baskets of bananas. Each basket has a random number of apples and bananas. The probability of you randomly picking up an apple is <span class=\"katex--inline\">\\frac13</span>, and the probability of you picking up an apple after picking up a banana is <span class=\"katex--inline\">\\frac{13}{27}</span>. If the probability of you picking up a banana after picking up an apple can be expressed as <span class=\"katex--inline\">\\frac{a}{b}</span>, where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are relatively prime, positive integers, compute <span class=\"katex--inline\">a+b</span>.</p>&#10;", "hints_md": "They died in 1761 and was English.", "hints_html": "<p>They died in 1761 and was English.</p>&#10;", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "1761 England", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}