{"status": "success", "data": {"description_md": "A frog sitting at the point $(1, 2)$ begins a sequence of jumps, where each jump is parallel to one of the coordinate axes and has length $1$, and the direction of each jump (up, down, right, or left) is chosen independently at random. The sequence ends when the frog reaches a side of the square with vertices $(0,0), (0,4), (4,4),$ and $(4,0)$. What is the probability that the sequence of jumps ends on a vertical side of the square$?$\n\n$\\textbf{(A) } \\frac{1}{2} \\qquad \\textbf{(B) } \\frac{5}{8} \\qquad \\textbf{(C) } \\frac{2}{3} \\qquad \\textbf{(D) } \\frac{3}{4} \\qquad \\textbf{(E) } \\frac{7}{8}$\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>A frog sitting at the point  <span class=\"katex--inline\">(1, 2)</span>  begins a sequence of jumps, where each jump is parallel to one of the coordinate axes and has length  <span class=\"katex--inline\">1</span> , and the direction of each jump (up, down, right, or left) is chosen independently at random. The sequence ends when the frog reaches a side of the square with vertices  <span class=\"katex--inline\">(0,0), (0,4), (4,4),</span>  and  <span class=\"katex--inline\">(4,0)</span> . What is the probability that the sequence of jumps ends on a vertical side of the square <span class=\"katex--inline\">?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } \\frac{1}{2} \\qquad \\textbf{(B) } \\frac{5}{8} \\qquad \\textbf{(C) } \\frac{2}{3} \\qquad \\textbf{(D) } \\frac{3}{4} \\qquad \\textbf{(E) } \\frac{7}{8}</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": "2020 AMC 12A Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc12A_p12", "prev": "/problem/20_amc12A_p10"}}