{"id":"aqua_rat:1f502a0be62d297df984f414a0e4a2dc","source_id":"aqua_rat","source_item_id":"1f502a0be62d297df984f414a0e4a2dc","external_id":null,"program":null,"section":"math","category_code":"PHM","category":"Preparing for Higher Math","subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":null,"scored":true,"layout_warning":null,"stem":"The events A and B are independent. The probability that event A occurs is 0.6, and the probability that at least one of the events A or B occurs is 0.96. What is the probability that event B occurs?","stimulus":"","stimulus_html":null,"stem_html":"<p>The events A and B are independent. The probability that event A occurs is 0.6, and the probability that at least one of the events A or B occurs is 0.96. What is the probability that event B occurs?</p>","rationale_html":"<p>Let x be the probability that B does not occur.</p><p>P(A and B do not occur) = 1 - 0.96 = 0.04</p><p>0.4x = 0.04</p><p>x=0.1</p><p>P(B occurs) = 1 - x = 0.9</p><p>The answer is E.</p>","correct_answer":["E"],"equiv_key":"d3ba57b4e4fdd7df69ad9df4","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>0.5</p>","ord":0},{"label":"B","content_html":"<p>0.6</p>","ord":1},{"label":"C","content_html":"<p>0.7</p>","ord":2},{"label":"D","content_html":"<p>0.8</p>","ord":3},{"label":"E","content_html":"<p>0.9</p>","ord":4}],"passage":null,"attribution":{"source_id":"aqua_rat","source_name":"AQuA-RAT algebra word problems with rationales","rights_holder":"Google DeepMind and the AQuA-RAT contributors","canonical_url":"https://github.com/google-deepmind/AQuA","retrieved_from":"https://raw.githubusercontent.com/google-deepmind/AQuA/master/","attribution":"Algebra word problems from the AQuA-RAT dataset (Ling et al., 2017), published by Google DeepMind under the Apache License 2.0.","disclaimer":"AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.","license":"Apache License 2.0. Crowdsourced by DeepMind and published for free use, including commercially.","redistributable":true,"item_count":508},"equivalents":[]}