{"id":"cb_question_bank:4af89aa1-f7eb-4094-bc0a-a8eb37dfb0b8","source_id":"cb_question_bank","source_item_id":"4af89aa1-f7eb-4094-bc0a-a8eb37dfb0b8","external_id":"b38bd503-bc4e-485d-a578-38da101ab31a","ibn":null,"question_id":"2df8f293","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.E.","skill":"Probability and conditional probability","difficulty":"M","score_band":4,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Each vertex of a 14 -sided polygon is labeled with one of the 14 letters upper A through upper N , with a different letter at each vertex. If one vertex is selected at random, what is the probability that the letter upper D will be at the selected vertex? (Express your answer as a decimal or fraction, not as a percent.)","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Each vertex of a <math alttext=\"14\"><mn>14</mn>\n</math>-sided polygon is labeled with one of the <math alttext=\"14\"><mn>14</mn>\n</math> letters <math alttext=\"upper A\"><mi>A</mi>\n</math> through <math alttext=\"upper N\"><mi>N</mi>\n</math>, with a different letter at each vertex. If one vertex is selected at random, what is the probability that the letter <math alttext=\"upper D\"><mi>D</mi>\n</math> will be at the selected vertex? (Express your answer as a decimal or fraction, not as a percent.)</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"one fourteenth\"><mfrac>\n\t<mn>1</mn>\n\t<mn>14</mn>\n</mfrac>\n</math>. If one vertex of the polygon is selected at random, the probability that the letter <math alttext=\"upper D\"><mi>D</mi>\n</math> will be at the selected vertex is equal to the number of vertices labeled with the letter <math alttext=\"upper D\"><mi>D</mi>\n</math> divided by the total number of vertices. It's given that each vertex is labeled with one of the <math alttext=\"14\"><mn>14</mn>\n</math> letters <math alttext=\"upper A\"><mi>A</mi>\n</math> through <math alttext=\"upper N\"><mi>N</mi>\n</math>, with a different letter at each vertex. It follows that there is <math alttext=\"1\"><mn>1</mn>\n</math> vertex labeled with the letter <math alttext=\"upper D\"><mi>D</mi>\n</math>. It's also given that the polygon is <math alttext=\"14\"><mn>14</mn>\n</math>-sided. It follows that there are a total of <math alttext=\"14\"><mn>14</mn>\n</math> vertices. Thus, the probability that the letter <math alttext=\"upper D\"><mi>D</mi>\n</math> will be at the selected vertex is <math alttext=\"one fourteenth\"><mfrac>\n\t<mn>1</mn>\n\t<mn>14</mn>\n</mfrac>\n</math>. Note that 1/14, .0714, and 0.071 are examples of ways to enter a correct answer.</p>","correct_answer":[".0714","1/14"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.835000+00:00","source_updated_at":"2023-08-02T20:25:59.835000+00:00","options":[],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}