{"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":"7f0ae4cc-1213-5ca1-a3c7-2be303fb4ae1","task_key":"counting~5fand~5fprobability--test--7f0ae4cc-1213-5ca1-a3c7-2be303fb4ae1","task_revision_id":"1","upstream_id":"","short_description":"A game of Plinko is played by dropping a ball at the top-middle of a set of…","config":"counting_and_probability","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"A game of Plinko is played by dropping a ball at the top-middle of a set of pegs. Each time the ball hits a peg, it has a $\\\\frac{1}{2}$ probability of deflecting either to the left or to the right. What is the probability that the ball lands in the middle slot as shown in the diagram (the red line)? [asy]\\nsize(3inch, 2.25inch);\\nfor (int i = 0; i < 8; i += 2) {\\n\\ndraw(circle((0, i + 1), 0.1));\\n\\ndraw(circle((2, i + 1), 0.1));\\n\\ndraw(circle((4, i + 1), 0.1));\\n\\ndraw(circle((6, i + 1), 0.1));\\n\\ndraw(circle((8, i + 1), 0.1));\\n\\ndraw(circle((10, i + 1), 0.1));\\n\\ndraw(circle((12, i + 1), 0.1));\\n\\ndraw(circle((14, i + 1), 0.1));\\n\\ndraw(circle((16, i + 1), 0.1));\\n\\ndraw(circle((1, i), 0.1));\\n\\ndraw(circle((3, i), 0.1));\\n\\ndraw(circle((5, i), 0.1));\\n\\ndraw(circle((7, i), 0.1));\\n\\ndraw(circle((9, i), 0.1));\\n\\ndraw(circle((11, i), 0.1));\\n\\ndraw(circle((13, i), 0.1));\\n\\ndraw(circle((15, i), 0.1));\\n}\\n\\npen target = red + linewidth(2);\\n\\ndraw((-0.8, -1)--(0.8, -1));\\ndraw((1.2, -1)--(2.8, -1));\\ndraw((3.2, -1)--(4.8, -1));\\ndraw((5.2, -1)--(6.8, -1));\\ndraw((7.2, -1)--(8.8, -1), target);\\ndraw((9.2, -1)--(10.8, -1));\\ndraw((11.2, -1)--(12.8, -1));\\ndraw((13.2, -1)--(14.8, -1));\\ndraw((15.2, -1)--(16.8, -1));\\n\\npen tube = black + linewidth(2);\\ndraw((7.2, 9)--(7.2, 7.8)--(8.8, 7.8)--(8.8, 9), tube);\\n\\nfilldraw(Circle((8, 8.5), 0.6), blue);\\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":[]}