{"status": "success", "data": {"description_md": "Three numbers in the interval $\\left[0,1\\right]$ are chosen independently and at random. What is the probability that the chosen numbers are the side lengths of a triangle with positive area?\n\n$\\textbf{(A)}\\ \\dfrac{1}{6}\\qquad\\textbf{(B)}\\ \\dfrac{1}{3}\\qquad\\textbf{(C)}\\ \\dfrac{1}{2}\\qquad\\textbf{(D)}\\ \\dfrac{2}{3}\\qquad\\textbf{(E)}\\ \\dfrac{5}{6}$\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>Three numbers in the interval  <span class=\"katex--inline\">\\left[0,1\\right]</span>  are chosen independently and at random. What is the probability that the chosen numbers are the side lengths of a triangle with positive area?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\dfrac{1}{6}\\qquad\\textbf{(B)}\\ \\dfrac{1}{3}\\qquad\\textbf{(C)}\\ \\dfrac{1}{2}\\qquad\\textbf{(D)}\\ \\dfrac{2}{3}\\qquad\\textbf{(E)}\\ \\dfrac{5}{6}</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": 5, "problem_name": "2016 AMC 12A Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12A_p24", "prev": "/problem/16_amc12A_p22"}}