{"status": "success", "data": {"description_md": "A fair $6$-sided die is repeatedly rolled until an odd number appears. What is the probability that every even number appears at least once before the first occurrence of an odd number?\n\n$\\textbf{(A)} ~\\frac{1}{120} \\qquad\\textbf{(B)} ~\\frac{1}{32} \\qquad\\textbf{(C)} ~\\frac{1}{20} \\qquad\\textbf{(D)} ~\\frac{3}{20} \\qquad\\textbf{(E)} ~\\frac{1}{6}$", "description_html": "<p>A fair  <span class=\"katex--inline\">6</span> -sided die is repeatedly rolled until an odd number appears. What is the probability that every even number appears at least once before the first occurrence of an odd number?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)} ~\\frac{1}{120} \\qquad\\textbf{(B)} ~\\frac{1}{32} \\qquad\\textbf{(C)} ~\\frac{1}{20} \\qquad\\textbf{(D)} ~\\frac{3}{20} \\qquad\\textbf{(E)} ~\\frac{1}{6}</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": "2021 AMC 10B Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc10B_p19", "prev": "/problem/21_amc10B_p17"}}