{"id":"cb_question_bank:8a69275d-7b92-4ac4-98ee-f3b858e835c8","source_id":"cb_question_bank","source_item_id":"8a69275d-7b92-4ac4-98ee-f3b858e835c8","external_id":"df56744a-4d13-4df3-a87c-06128770af34","ibn":null,"question_id":"6a715bed","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.E.","skill":"Probability and conditional probability","difficulty":"H","score_band":7,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The table summarizes the distribution of age and assigned group for 90 participants in a study. 0 – 9 years 10 – 19 years 20 plus years Total Group A 7 14 9 30 Group B 6 4 20 30 Group C 17 12 1 30 Total 30 30 30 90 One of these participants will be selected at random. What is the probability of selecting a participant from group A, given that the participant is at least 10 years of age? (Express your answer as a decimal or fraction, not as a percent.)","stimulus":"","stimulus_html":null,"stem_html":"

The table summarizes the distribution of age and assigned group for 90\n participants in a study.

\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 0\n–9\n years10\n–19\n years20+ yearsTotal
Group A7\n14\n9\n30\n
Group B6\n4\n20\n30\n
Group C17\n12\n1\n30\n
Total30\n30\n30\n90\n
\n

One of these participants will be selected at random. What is the probability of selecting a participant from group A, given that the participant is at least 10\n years of age? (Express your answer as a decimal or fraction, not as a percent.)

","rationale_html":"

The correct answer is \n\t23\n\t60\n\n. It's given that one of the participants will be selected at random. The probability of selecting a participant from group A given that the participant is at least 10\n years of age is the number of participants in group A who are at least 10\n years of age divided by the total number of participants who are at least 10\n years of age. The table shows that in group A, there are 14\n participants who are 10\n–19\n years of age and 9\n participants who are 20+ years of age. Therefore, there are 14+9, or 23\n, participants in group A who are at least 10\n years of age. The table also shows that there are a total of 30\n participants who are 10\n–19\n years of age and 30\n participants who are 20+ years of age. Therefore, there are a total of 30+30, or 60\n, participants who are at least 10\n years of age. It follows that the probability of selecting a participant from group A given that the participant is at least 10\n years of age is \n\t23\n\t60\n\n. Note that 23/60, .3833, and 0.383 are examples of ways to enter a correct answer.

","correct_answer":[".3833","23/60"],"has_media":false,"has_mathml":true,"has_table":true,"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}}