{"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":"82edac7d-5327-5b29-b042-9da5c021cfe4","task_key":"counting~5fand~5fprobability--test--82edac7d-5327-5b29-b042-9da5c021cfe4","task_revision_id":"1","upstream_id":"","short_description":"Two circles with spinners at their centers are divided into three equal regions…","config":"counting_and_probability","split":"test","body":"{\"level\":\"Level 2\",\"problem\":\"Two circles with spinners at their centers are divided into three equal regions as shown. When both spinners are spun, what is the probability that the product of the two values is negative? Express your answer as a common fraction. [asy]\\nsize(140);\\nvoid spinner(picture pic=currentpicture, real rotate, int a, int b, int c)\\n{\\ndot(pic,(0,0),linewidth(4));\\ndraw(pic, unitcircle ^^ (0,0)--dir(90+rotate) ^^ (0,0)--dir(210+rotate) ^^ (0,0)--dir(-30+rotate));\\nlabel(pic, \\\"$\\\"+string(a)+\\\"$\\\",dir(30+rotate)/2,fontsize(10pt));\\nlabel(pic, \\\"$\\\"+string(b)+\\\"$\\\",dir(150+rotate)/2,fontsize(10pt));\\nlabel(pic, \\\"$\\\"+string(c)+\\\"$\\\",dir(-90+rotate)/2,fontsize(10pt));\\n}\\npicture p;\\nspinner(0,-1,-3,5); spinner(p,180,2,4,-6);\\ndraw((0,0)--dir(-10)/2,EndArrow(4)); draw(p,(0,0)--dir(-75)/2,EndArrow(4)); add(shift(2.5*right)*p);[/asy]\",\"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":[]}