{"status": "success", "data": {"description_md": "Tina randomly selects two distinct numbers from the set $\\{1, 2, 3, 4, 5\\}$, and Sergio randomly selects a number from the set $\\{1, 2, \\ldots, 10\\}$. What is the probability that Sergio's number is larger than the sum of the two numbers chosen by Tina? \n\n$\\text{(A)}\\ 2/5 \\qquad \\text{(B)}\\ 9/20 \\qquad \\text{(C)}\\ 1/2 \\qquad \\text{(D)}\\ 11/20 \\qquad \\text{(E)}\\ 24/25$\n___\nFull 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>Tina randomly selects two distinct numbers from the set  <span class=\"katex--inline\">\\{1, 2, 3, 4, 5\\}</span> , and Sergio randomly selects a number from the set  <span class=\"katex--inline\">\\{1, 2, \\ldots, 10\\}</span> . What is the probability that Sergio&#8217;s number is larger than the sum of the two numbers chosen by Tina?</p>&#10;<p> <span class=\"katex--inline\">\\text{(A)}\\ 2/5 \\qquad \\text{(B)}\\ 9/20 \\qquad \\text{(C)}\\ 1/2 \\qquad \\text{(D)}\\ 11/20 \\qquad \\text{(E)}\\ 24/25</span> </p>&#10;<hr><p>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": "2002 AMC 12A Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc12A_p17", "prev": "/problem/02_amc12A_p15"}}