{"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":"aa557416-3735-5ea3-b163-4e4e51edda03","task_key":"counting~5fand~5fprobability--test--aa557416-3735-5ea3-b163-4e4e51edda03","task_revision_id":"1","upstream_id":"","short_description":"Regions $A, B, C, J$ and $K$ represent ponds. Logs leave pond $A$ and float down…","config":"counting_and_probability","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Regions $A, B, C, J$ and $K$ represent ponds. Logs leave pond $A$ and float down flumes (represented by arrows) to eventually end up in pond $B$ or pond $C$. On leaving a pond, the logs are equally likely to use any available exit flume. Logs can only float in the direction the arrow is pointing. What is the probability that a log in pond $A$ will end up in pond $B$? Express your answer as a common fraction.\\n\\n[asy]\\nlabel(\\\"$A$\\\",(10,22),S);\\nlabel(\\\"$B$\\\",(10,2),S);\\nlabel(\\\"$C$\\\",(10,-7),S);\\nlabel(\\\"$J$\\\",(2,13),S);\\nlabel(\\\"$K$\\\",(10,12),S);\\npath a=(10,-10)..(20,0)--(0,0)..cycle;\\npath b=(10,-7)..(3,0)--(17,0)..cycle;\\ndraw(a);\\ndraw(b);\\nfill((3.1,0.1)--(16.9,0.1)--(16.9,-0.1)--(3.1,-0.1)--cycle,white);\\ndraw(Circle((10,0),3));\\ndraw(Circle((10,10),3));\\ndraw(Circle((10,20),3));\\ndraw((10,16.9)--(10,13.1),Arrow);\\ndraw((10,6.9)--(10,3.1),Arrow);\\ndraw(Circle((2,10),3));\\ndraw((2,7)--(2.5,0),Arrow);\\ndraw((1.5,7)--(0.2,0),Arrow);\\ndraw((10,16.9)--(2,13.2),Arrow);\\ndraw((10,16.9)--(19.8,0),Arrow);\\ndraw((10,6.9)--(17.2,0),Arrow);\\ndraw((3,8)--(10,3.1),Arrow);\\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":[]}