{"status": "success", "data": {"description_md": "Cyrus the frog jumps $2$ units in a direction, then $2$ more in another direction. What is the probability that he lands less than $1$ unit away from his starting position?\n\n$\\textbf{(A)}~\\frac{1}{6}\\qquad\\textbf{(B)}~\\frac{1}{5}\\qquad\\textbf{(C)}~\\frac{\\sqrt{3}}{8}\\qquad\\textbf{(D)}~\\frac{\\arctan \\frac{1}{2}}{\\pi}\\qquad\\textbf{(E)}~\\frac{2\\arcsin \\frac{1}{4}}{\\pi}$\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>Cyrus the frog jumps  <span class=\"katex--inline\">2</span>  units in a direction, then  <span class=\"katex--inline\">2</span>  more in another direction. What is the probability that he lands less than  <span class=\"katex--inline\">1</span>  unit away from his starting position?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}~\\frac{1}{6}\\qquad\\textbf{(B)}~\\frac{1}{5}\\qquad\\textbf{(C)}~\\frac{\\sqrt{3}}{8}\\qquad\\textbf{(D)}~\\frac{\\arctan \\frac{1}{2}}{\\pi}\\qquad\\textbf{(E)}~\\frac{2\\arcsin \\frac{1}{4}}{\\pi}</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": "2023 AMC 12B Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc12B_p21", "prev": "/problem/23_amc12B_p19"}}