{"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":"a6fbc406-2f6f-5281-93e2-720c649d49cb","task_key":"counting~5fand~5fprobability--test--a6fbc406-2f6f-5281-93e2-720c649d49cb","task_revision_id":"1","upstream_id":"","short_description":"A European train compartment has six seats. Four of the seats are broken.…","config":"counting_and_probability","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"A European train compartment has six seats.  Four of the seats are broken.  Wilhelm needs to fill out a form like the one here to indicate that there are broken seats.  If he randomly checks off four of the seats in the diagram, what is the probability that he marked the correct seats?  Express your answer as a common fraction.\\n\\n[asy]\\n\\ndraw((0,0)--(24,0)--(24,18)--(0,18)--(0,0));\\n\\nlabel(\\\"$\\\\textbf{Maintenance Report}$\\\",(12,16));\\n\\ndraw((2,2)--(22,2)--(22,14)--(2,14)--(2,2));\\n\\ndraw((4,4)--(8,4)--(8,6)--(4,6)--(4,4));\\n\\ndraw((10,4)--(14,4)--(14,6)--(10,6)--(10,4));\\nlabel(\\\"$\\\\surd$\\\",(12,5));\\n\\ndraw((16,4)--(20,4)--(20,6)--(16,6)--(16,4));\\nlabel(\\\"$\\\\surd$\\\",(18,5));\\n\\ndraw((4,10)--(8,10)--(8,12)--(4,12)--(4,10));\\nlabel(\\\"$\\\\surd$\\\",(6,11));\\n\\ndraw((10,10)--(14,10)--(14,12)--(10,12)--(10,10));\\nlabel(\\\"$\\\\surd$\\\",(12,11));\\n\\ndraw((16,10)--(20,10)--(20,12)--(16,12)--(16,10));\\n\\n[/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":[]}