{"status": "success", "data": {"description_md": "Jen randomly picks $4$ distinct elements from $\\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\\}$. The lottery machine also picks $4$ distinct elements. If the lottery machine picks at least $2$ of Jen's numbers, Jen wins a prize. If the lottery machine's numbers are all $4$ of Jen's, Jen wins the Grand Prize. Given that Jen wins a prize, what is the probability she wins a Grand Prize?\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Jen randomly picks <span class=\"katex--inline\">4</span> distinct elements from <span class=\"katex--inline\">\\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\\}</span>. The lottery machine also picks <span class=\"katex--inline\">4</span> distinct elements. If the lottery machine picks at least <span class=\"katex--inline\">2</span> of Jen&#8217;s numbers, Jen wins a prize. If the lottery machine&#8217;s numbers are all <span class=\"katex--inline\">4</span> of Jen&#8217;s, Jen wins the Grand Prize. Given that Jen wins a prize, what is the probability she wins a Grand Prize?</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2024 AIME I Problem 4", "can_next": true, "can_prev": true, "nxt": "/problem/24_aime_I_p05", "prev": "/problem/24_aime_I_p03"}}