{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"5caff8d8-8a03-5348-85bd-b1612ec9bb4c","task_key":"counting~5fand~5fprobability--test--5caff8d8-8a03-5348-85bd-b1612ec9bb4c","task_revision_id":"1","upstream_id":"","short_description":"When rolling a certain unfair six-sided die with faces numbered 1, 2, 3, 4, 5,…","config":"counting_and_probability","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"When rolling a certain unfair six-sided die with faces numbered 1, 2, 3, 4, 5, and 6, the probability of obtaining face $F$ is greater than $1/6$, the probability of obtaining the face opposite face $F$ is less than $1/6$, the probability of obtaining each of the other faces is $1/6$, and the sum of the numbers on each pair of opposite faces is 7. When two such dice are rolled, the probability of obtaining a sum of 7 is $ \\\\frac{47}{288} $. Given that the probability of obtaining face $F$ is $m/n$, where $m$ and $n$ are relatively prime positive integers, find $m+n$.\",\"type\":\"Counting & Probability\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}