{"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 $\\{1, 2, ..., 10\\}$. The probability that Sergio's number is larger than the sum of the two numbers chosen by Tina is\n\n$\\text{(A)}\\ \\dfrac25 \\qquad \\text{(B)}\\ \\dfrac9{20} \\qquad \\text{(C)}\\ \\dfrac12 \\qquad \\text{(D)}\\ \\dfrac{11}{20} \\qquad \\text{(E)}\\ \\dfrac{24}{25}$", "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, ..., 10\\}</span>. The probability that Sergio&#8217;s number is larger than the sum of the two numbers chosen by Tina is</p>&#10;<p><span class=\"katex--inline\">\\text{(A)}\\ \\dfrac25 \\qquad \\text{(B)}\\ \\dfrac9{20} \\qquad \\text{(C)}\\ \\dfrac12 \\qquad \\text{(D)}\\ \\dfrac{11}{20} \\qquad \\text{(E)}\\ \\dfrac{24}{25}</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2002 AMC 10A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc10A_p25", "prev": "/problem/02_amc10A_p23"}}