{"status": "success", "data": {"description_md": "A frog makes $3$ jumps, each exactly $1$ meter long. The directions of the jumps are chosen independently at random. What is the probability that the frog's final position is no more than $1$ meter from its starting position?\n\n$\\textbf{(A)}\\ \\dfrac{1}{6} \\qquad \\textbf{(B)}\\ \\dfrac{1}{5} \\qquad \\textbf{(C)}\\ \\dfrac{1}{4} \\qquad \\textbf{(D)}\\ \\dfrac{1}{3} \\qquad \\textbf{(E)}\\ \\dfrac{1}{2}$\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 makes  <span class=\"katex--inline\">3</span>  jumps, each exactly  <span class=\"katex--inline\">1</span>  meter long. The directions of the jumps are chosen independently at random. What is the probability that the frog&#8217;s final position is no more than  <span class=\"katex--inline\">1</span>  meter from its starting position?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\dfrac{1}{6} \\qquad \\textbf{(B)}\\ \\dfrac{1}{5} \\qquad \\textbf{(C)}\\ \\dfrac{1}{4} \\qquad \\textbf{(D)}\\ \\dfrac{1}{3} \\qquad \\textbf{(E)}\\ \\dfrac{1}{2}</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": "2010 AMC 12B Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc12B_p19", "prev": "/problem/10_amc12B_p17"}}