{"status": "success", "data": {"description_md": "An urn contains one red ball and one blue ball. A box of extra red and blue balls lie nearby. George performs the following operation four times: he draws a ball from the urn at random and then takes a ball of the same color from the box and returns those two matching balls to the urn. After the four iterations the urn contains six balls. What is the probability that the urn contains three balls of each color?\n\n$\\textbf{(A) } \\frac16 \\qquad \\textbf{(B) }\\frac15 \\qquad \\textbf{(C) } \\frac14 \\qquad \\textbf{(D) } \\frac13 \\qquad \\textbf{(E) } \\frac12$\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>An urn contains one red ball and one blue ball. A box of extra red and blue balls lie nearby. George performs the following operation four times: he draws a ball from the urn at random and then takes a ball of the same color from the box and returns those two matching balls to the urn. After the four iterations the urn contains six balls. What is the probability that the urn contains three balls of each color?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } \\frac16 \\qquad \\textbf{(B) }\\frac15 \\qquad \\textbf{(C) } \\frac14 \\qquad \\textbf{(D) } \\frac13 \\qquad \\textbf{(E) } \\frac12</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": "2020 AMC 12B Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc12B_p17", "prev": "/problem/20_amc12B_p15"}}