{"status": "success", "data": {"description_md": "A coin is altered so that the probability that it lands on heads is less than $\\frac{1}{2}$ and when the coin is flipped four times, the probability of an equal number of heads and tails is $\\frac{1}{6}$. What is the probability that the coin lands on heads?\n\n$\\textbf{(A)}\\ \\frac{\\sqrt{15}-3}{6} \\qquad \\textbf{(B)}\\ \\frac{6-\\sqrt{6\\sqrt{6}+2}}{12} \\qquad \\textbf{(C)}\\ \\frac{\\sqrt{2}-1}{2} \\qquad \\textbf{(D)}\\ \\frac{3-\\sqrt{3}}{6} \\qquad \\textbf{(E)}\\ \\frac{\\sqrt{3}-1}{2}$\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>A coin is altered so that the probability that it lands on heads is less than  <span class=\"katex--inline\">\\frac{1}{2}</span>  and when the coin is flipped four times, the probability of an equal number of heads and tails is  <span class=\"katex--inline\">\\frac{1}{6}</span> . What is the probability that the coin lands on heads?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{\\sqrt{15}-3}{6} \\qquad \\textbf{(B)}\\ \\frac{6-\\sqrt{6\\sqrt{6}+2}}{12} \\qquad \\textbf{(C)}\\ \\frac{\\sqrt{2}-1}{2} \\qquad \\textbf{(D)}\\ \\frac{3-\\sqrt{3}}{6} \\qquad \\textbf{(E)}\\ \\frac{\\sqrt{3}-1}{2}</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": "2010 AMC 12A Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc12A_p16", "prev": "/problem/10_amc12A_p14"}}