{"id":"cb_question_bank:020b9ae1-5ddb-408e-8e3b-edfa3dde10f9","source_id":"cb_question_bank","source_item_id":"020b9ae1-5ddb-408e-8e3b-edfa3dde10f9","external_id":null,"ibn":"070628-DC","question_id":"e29586d5","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":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Number of Contestants by Score and Day 5 out of 5 4 out of 5 3 out of 5 2 out of 5 1 out of 5 0 out of 5 Total Day 1 2 3 4 6 2 3 20 Day 2 2 3 5 5 4 1 20 Day 3 3 3 4 5 3 2 20 Total 7 9 13 16 9 6 60 The same 20 contestants, on each of 3 days, answered 5 questions in order to win a prize. Each contestant received 1 point for each correct answer. The number of contestants receiving a given score on each day is shown in the table above. No contestant received the same score on two different days. If a contestant is selected at random, what is the probability that the selected contestant received a score of 5 on Day 2 or Day 3, given that the contestant received a score of 5 on one of the three days?","stimulus":"","stimulus_html":null,"stem_html":"
Number of Contestants by Score and Day
 5 out
  of 5		4 out
  of 5		3 out
  of 5		2 out
  of 5		1 out
  of 5		0 out
  of 5		Total
Day 123462320
Day 223554120
Day 333453220
Total7913169660

The same 20 contestants, on each of 3 days, answered 5 questions in order to win a prize. Each contestant received 1 point for each correct answer. The number of contestants receiving a given score on each day is shown in the table above.

No contestant received the same score on two different days. If a contestant is selected at random, what is the probability that the selected contestant received a score of 5 on Day 2 or Day 3, given that the contestant received a score of 5 on one of the three days?

\n","rationale_html":"

The correct answer is \"five. It is given that no contestant received the same score on two different days, so each of the contestants who received a score of 5 is represented in the “5 out of 5” column of the table exactly once. Therefore, the probability of selecting a contestant who received a score of 5 on Day 2 or Day 3, given that the contestant received a score of 5 on one of the three days, is found by dividing the total number of contestants who received a score of 5 on Day 2 or Day 3 \"2 by the total number of contestants who received a score of 5, which is given in the table as 7. So the probability is \"five. Note that 5/7, .7142, .7143, and 0.714 are examples of ways to enter a correct answer.

\n","correct_answer":["5/7"],"has_media":true,"has_mathml":false,"has_table":true,"source_created_at":"2023-08-02T20:25:59.632000+00:00","source_updated_at":"2023-08-02T20:25:59.632000+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}}