{"status": "success", "data": {"description_md": "Tom, Dick, and Harry are playing a game. Starting at the same time, each of them flips a fair coin repeatedly until he gets his first head, at which point he stops. What is the probability that all three flip their coins the same number of times?\n\n$\\textbf{(A)}\\ \\frac{1}{8} \\qquad<br>\\textbf{(B)}\\ \\frac{1}{7} \\qquad<br>\\textbf{(C)}\\ \\frac{1}{6} \\qquad<br>\\textbf{(D)}\\ \\frac{1}{4} \\qquad<br>\\textbf{(E)}\\ \\frac{1}{3}$\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>Tom, Dick, and Harry are playing a game. Starting at the same time, each of them flips a fair coin repeatedly until he gets his first head, at which point he stops. What is the probability that all three flip their coins the same number of times?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{1}{8} \\qquad\\textbf{(B)}\\ \\frac{1}{7} \\qquad\\textbf{(C)}\\ \\frac{1}{6} \\qquad\\textbf{(D)}\\ \\frac{1}{4} \\qquad\\textbf{(E)}\\ \\frac{1}{3}</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": "2016 AMC 12B Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12B_p20", "prev": "/problem/16_amc12B_p18"}}