{"status": "success", "data": {"description_md": "Abby, Bernardo, Carl, and Debra play a game in which each of them starts with four coins. The game consists of four rounds. In each round, four balls are placed in an urn---one green, one red, and two white. The players each draw a ball at random without replacement. Whoever gets the green ball gives one coin to whoever gets the red ball. What is the probability that, at the end of the fourth round, each of the players has four coins?\n\n$\\textbf{(A)}\\ \\frac{7}{576} \\qquad \\textbf{(B)}\\ \\frac{5}{192} \\qquad \\textbf{(C)}\\ \\frac{1}{36} \\qquad \\textbf{(D)}\\ \\frac{5}{144} \\qquad\\textbf{(E)}\\ \\frac{7}{48}$\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>Abby, Bernardo, Carl, and Debra play a game in which each of them starts with four coins. The game consists of four rounds. In each round, four balls are placed in an urn&#8212;one green, one red, and two white. The players each draw a ball at random without replacement. Whoever gets the green ball gives one coin to whoever gets the red ball. What is the probability that, at the end of the fourth round, each of the players has four coins?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{7}{576} \\qquad \\textbf{(B)}\\ \\frac{5}{192} \\qquad \\textbf{(C)}\\ \\frac{1}{36} \\qquad \\textbf{(D)}\\ \\frac{5}{144} \\qquad\\textbf{(E)}\\ \\frac{7}{48}</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": 5, "problem_name": "2017 AMC 12B Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc12B_p23", "prev": "/problem/17_amc12B_p21"}}