{"status": "success", "data": {"description_md": "A red ball and a green ball are randomly and independently tossed into bins numbered with positive integers so that for each ball, the probability that it is tossed into bin $k$ is $2^{-k}$ for $k=1,2,3,\\ldots.$ What is the probability that the red ball is tossed into a higher-numbered bin than the green ball?\n\n$\\textbf{(A) } \\frac{1}{4} \\qquad\\textbf{(B) } \\frac{2}{7} \\qquad\\textbf{(C) } \\frac{1}{3} \\qquad\\textbf{(D) } \\frac{3}{8} \\qquad\\textbf{(E) } \\frac{3}{7}$", "description_html": "<p>A red ball and a green ball are randomly and independently tossed into bins numbered with positive integers so that for each ball, the probability that it is tossed into bin  <span class=\"katex--inline\">k</span>  is  <span class=\"katex--inline\">2^{-k}</span>  for  <span class=\"katex--inline\">k=1,2,3,\\ldots.</span>  What is the probability that the red ball is tossed into a higher-numbered bin than the green ball?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } \\frac{1}{4} \\qquad\\textbf{(B) } \\frac{2}{7} \\qquad\\textbf{(C) } \\frac{1}{3} \\qquad\\textbf{(D) } \\frac{3}{8} \\qquad\\textbf{(E) } \\frac{3}{7}</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": "2019 AMC 10B Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc10B_p18", "prev": "/problem/19_amc10B_p16"}}