{"status": "success", "data": {"description_md": "Sonya the frog chooses a point uniformly at random lying within the square\n$[0, 6]$ $\\times$ $[0, 6]$ in the coordinate plane and hops to that point. She then randomly\nchooses a distance uniformly at random from $[0, 1]$ and a direction uniformly at\nrandom from {north, south, east, west}. All her choices are independent. She now\nhops the distance in the chosen direction. What is the probability that she lands\noutside the square?\n\n$\\textbf{(A) } \\frac{1}{6} \\qquad \\textbf{(B) } \\frac{1}{12} \\qquad \\textbf{(C) } \\frac{1}{4} \\qquad \\textbf{(D) } \\frac{1}{10} \\qquad \\textbf{(E) } \\frac{1}{9}$", "description_html": "<p>Sonya the frog chooses a point uniformly at random lying within the square<br/>\n <span class=\"katex--inline\">[0, 6]</span>   <span class=\"katex--inline\">\\times</span>   <span class=\"katex--inline\">[0, 6]</span>  in the coordinate plane and hops to that point. She then randomly<br/>\nchooses a distance uniformly at random from  <span class=\"katex--inline\">[0, 1]</span>  and a direction uniformly at<br/>\nrandom from {north, south, east, west}. All her choices are independent. She now<br/>\nhops the distance in the chosen direction. What is the probability that she lands<br/>\noutside the square?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } \\frac{1}{6} \\qquad \\textbf{(B) } \\frac{1}{12} \\qquad \\textbf{(C) } \\frac{1}{4} \\qquad \\textbf{(D) } \\frac{1}{10} \\qquad \\textbf{(E) } \\frac{1}{9}</span> </p>\n<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 10B Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc10B_p20", "prev": "/problem/23_amc10B_p18"}}