{"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":"7424fd82-4472-5e33-91d0-2f8dbfe6bc30","task_key":"counting~5fand~5fprobability--test--7424fd82-4472-5e33-91d0-2f8dbfe6bc30","task_revision_id":"1","upstream_id":"","short_description":"Beginning at point $A$ in the diagram below, Dora selects one of the four…","config":"counting_and_probability","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Beginning at point $A$ in the diagram below, Dora selects one of the four possible directions with equal probability. Each time she comes to an intersection, she again randomly selects one of the possible directions. What is the probability that, in her first four steps, she will walk completely around the gray square? Express your answer as a common fraction. [asy]size(100);\\nfill((1,1)--(1,2)--(2,2)--(2,1)--cycle, gray(.6));\\ndraw((0,0)--(0,3)--(3,3)--(3,0)--cycle, linewidth(1.5));\\ndraw((0,1)--(3,1), linewidth(1.5));\\ndraw((0,2)--(3,2), linewidth(1.5));\\ndraw((1,0)--(1,3), linewidth(1.5));\\ndraw((2,0)--(2,3), linewidth(1.5));\\ndot(MP(\\\"A\\\", (1,2), NW));\\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":[]}