{"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$\\textbf{(A)}\\ \\frac12\\qquad\\textbf{(B)}\\ \\frac 58\\qquad\\textbf{(C)}\\ \\frac 23\\qquad\\textbf{(D)}\\ \\frac34\\qquad\\textbf{(E)}\\ \\frac 78$", "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?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ \\frac12\\qquad\\textbf{(B)}\\ \\frac 58\\qquad\\textbf{(C)}\\ \\frac 23\\qquad\\textbf{(D)}\\ \\frac34\\qquad\\textbf{(E)}\\ \\frac 78</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2020 AMC 10A Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc10A_p14", "prev": "/problem/20_amc10A_p12"}}