{"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":"8a4055ec-d871-5b75-8fef-8eb9ab477df8","task_key":"counting~5fand~5fprobability--test--8a4055ec-d871-5b75-8fef-8eb9ab477df8","task_revision_id":"1","upstream_id":"","short_description":"Bag A contains $3$ white and $2$ red balls. Bag B contains $6$ white and $3$ red…","config":"counting_and_probability","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Bag A contains $3$ white and $2$ red balls. Bag B contains $6$ white and $3$ red balls. One of the two bags will be chosen at random, and then two balls will be drawn from that bag at random without replacement. What is the probability that the two balls drawn will be the same color? Express your answer as a common fraction. [asy] size(140); defaultpen(linewidth(0.7)); pen darkness = linewidth(1.2);\\nreal r = 0.642;\\nfilldraw(circle((-0.931,2.701),r),gray(0.5));\\n\\nfilldraw(circle((1.534,2.633),r),white,darkness);\\n\\nfilldraw(circle((0.356,2.842),r),white,darkness);\\n\\nfilldraw(circle((1.026,2.385),r),gray(0.5));\\n\\nfilldraw(circle((-0.184,2.502),r),white,darkness);\\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":[]}