{"id":"aqua_rat:2a898f0fa48d7ebd8011538c5ed4bc14","source_id":"aqua_rat","source_item_id":"2a898f0fa48d7ebd8011538c5ed4bc14","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":"A picks a number from the bag where the bag consists of numbers from 1,2....23 and puts it in the same bag. Now, another person B picks a number from the bag. Find the probability that A has picked a greater number than B?","stimulus":"","stimulus_html":null,"stem_html":"<p>A picks a number from the bag where the bag consists of numbers from 1,2....23 and puts it in the same bag. Now, another person B picks a number from the bag. Find the probability that A has picked a greater number than B?</p>","rationale_html":"<p>If Ram draws 1, then Sam can draw anything from 2 to 23 = 22 ways</p><p>If Ram draws 2, then Sam can draw anything from 3 to 23 = 21 ways</p><p>. . . .</p><p>. . . .</p><p>If Ram draws 23, Sam&#x27;s number of option = 0 ways.</p><p>Total required ways = 22 + 21 + 20 + . . . . + 0 = 22×232 = 253</p><p>Total ways of drawing two cards = 23×23</p><p>Required probability = 253/529=11/23</p><p>C</p>","correct_answer":["C"],"equiv_key":"aa9b439c700cc1ef6e485efe","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>10/23</p>","ord":0},{"label":"B","content_html":"<p>12/23</p>","ord":1},{"label":"C","content_html":"<p>11/23</p>","ord":2},{"label":"D","content_html":"<p>13/23</p>","ord":3},{"label":"E","content_html":"<p>15/23</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":[]}