{"id":"cb_question_bank:d7b6e042-1068-4911-953c-ba6791984b53","source_id":"cb_question_bank","source_item_id":"d7b6e042-1068-4911-953c-ba6791984b53","external_id":"ccd77c85-b9f7-42eb-9d6f-78971c82adf8","ibn":null,"question_id":"b8150b17","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.E.","skill":"Probability and conditional probability","difficulty":"E","score_band":1,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"For a particular machine that produces beads, 29 out of every 100 beads it produces have a defect. A bead produced by the machine will be selected at random. What is the probability of selecting a bead that has a defect?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">For a particular machine that produces beads, <math alttext=\"29\"><mn>29</mn>\n</math> out of every <math alttext=\"100\"><mn>100</mn>\n</math> beads it produces have a defect. A bead produced by the machine will be selected at random. What is the probability of selecting a bead that has a defect?</p>","rationale_html":"<p style=\"text-align: left;\">Choice C is correct. It’s given that <math alttext=\"29\"><mn>29</mn>\n</math> out of every <math alttext=\"100\"><mn>100</mn>\n</math> beads that the machine produces have a defect. It follows that if the machine produces <math alttext=\"k\"><mi>k</mi>\n</math> beads, then the number of beads that have a defect is <math alttext=\"StartFraction 29 Over 100 EndFraction k\"><mfrac><mn>29</mn><mn>100</mn></mfrac><mi>k</mi></math>, for some constant <math alttext=\"k\"><mi>k</mi>\n</math>. If a bead produced by the machine will be selected at random, the probability of selecting a bead that has a defect is given by the number of beads with a defect, <math alttext=\"StartFraction 29 Over 100 EndFraction k\"><mfrac><mn>29</mn><mn>100</mn></mfrac><mi>k</mi></math>, divided by the number of beads produced by the machine, <math alttext=\"k\"><mi>k</mi>\n</math>. Therefore, the probability of selecting a bead that has a defect is <math alttext=\"StartStartFraction StartFraction 29 Over 100 EndFraction k OverOver k EndEndFraction\"><mfrac><mrow><mstyle displaystyle=\"true\"><mfrac><mn>29</mn><mn>100</mn></mfrac></mstyle><mi>k</mi></mrow><mi>k</mi></mfrac></math>, or <math alttext=\"StartFraction 29 Over 100 EndFraction\"><mfrac><mn>29</mn><mn>100</mn></mfrac></math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual or computational errors.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual or computational errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or computational errors.</p>","correct_answer":["C"],"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":[{"label":"A","content_html":"<p><math alttext=\"StartFraction 1 Over 2,900 EndFraction\"><mfrac>\n\t<mn>1</mn>\n\t<mn>2,900</mn>\n</mfrac>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"one twenty ninth\"><mfrac>\n\t<mn>1</mn>\n\t<mn>29</mn>\n</mfrac>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"StartFraction 29 Over 100 EndFraction\"><mfrac>\n\t<mn>29</mn>\n\t<mn>100</mn>\n</mfrac>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"StartFraction 29 Over 10 EndFraction\"><mfrac>\n\t<mn>29</mn>\n\t<mn>10</mn>\n</mfrac>\n</math></p>","ord":3}],"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}}