{"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":"cbb712fb-ea30-5074-b456-6e88993f3dd3","task_key":"counting~5fand~5fprobability--test--cbb712fb-ea30-5074-b456-6e88993f3dd3","task_revision_id":"1","upstream_id":"","short_description":"The wheel shown is spun twice, so that the numbers indicated by the pointer are…","config":"counting_and_probability","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"The wheel shown is spun twice, so that the numbers indicated by the pointer are randomly determined (with each number on the wheel being equally likely). The two numbers determined in this way are recorded. The first number is divided by 4, determining one of the remainders 1,2,3 marking the columns of the checkerboard shown. The second number is divided by 5, determining one of the remainders 1,2,3,4 marking the rows of the checkerboard. Finally, a checker is placed on the square where this column and row meet. What is the probability that the checker is placed on a shaded square of the checkerboard?\\n\\n[asy]\\nunitsize(1cm);\\ndraw(Circle((0,0),2),linewidth(0.7));\\ndraw((1.7,1)--(-1.7,-1),linewidth(0.7));\\ndraw((1.7,-1)--(-1.7,1),linewidth(0.7));\\ndraw((0,2)--(0,-2));\\nlabel(\\\"1\\\",(0.8,0.5),NW);\\nlabel(\\\"2\\\",(0.8,-0.5),SW);\\nlabel(\\\"6\\\",(-0.8,0.5),NE);\\nlabel(\\\"9\\\",(-0.8,-0.5),SE);\\nlabel(\\\"3\\\",(-0.7,0),W);\\nlabel(\\\"7\\\",(0.7,0),E);\\ndraw((-2.8,0)--(-2.1,0),Arrow);\\nlabel(\\\"Pointer\\\",(-2.8,0),W);\\nfill((3,0)--(3,1)--(4,1)--(4,0)--cycle,gray(0.7));\\nfill((3,-2)--(3,-1)--(4,-1)--(4,-2)--cycle,gray(0.7));\\nfill((4,1)--(4,2)--(5,2)--(5,1)--cycle,gray(0.7));\\nfill((4,-1)--(4,0)--(5,0)--(5,-1)--cycle,gray(0.7));\\nfill((5,0)--(5,1)--(6,1)--(6,0)--cycle,gray(0.7));\\nfill((5,-2)--(5,-1)--(6,-1)--(6,-2)--cycle,gray(0.7));\\ndraw((3,-2)--(3,2)--(6,2)--(6,-2)--cycle,linewidth(0.7));\\ndraw((3,-1)--(6,-1),linewidth(0.7));\\ndraw((3,0)--(6,0),linewidth(0.7));\\ndraw((3,1)--(6,1),linewidth(0.7));\\ndraw((4,-2)--(4,2),linewidth(0.7));\\ndraw((5,-2)--(5,2),linewidth(0.7));\\nlabel(\\\"1\\\",(3.5,-2),S);\\nlabel(\\\"2\\\",(4.5,-2),S);\\nlabel(\\\"3\\\",(5.5,-2),S);\\nlabel(\\\"1\\\",(3,-1.5),W);\\nlabel(\\\"2\\\",(3,-0.5),W);\\nlabel(\\\"3\\\",(3,0.5),W);\\nlabel(\\\"4\\\",(3,1.5),W);\\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":[]}