{"status": "success", "data": {"description_md": "Twelve fair dice are rolled. What is the probability that the product of the numbers on the top faces is prime?\n\n$\\mathrm{(A)} \\left(\\frac{1}{12}\\right)^{12} \\qquad \\mathrm{(B)} \\left(\\frac{1}{6}\\right)^{12} \\qquad \\mathrm{(C)} 2\\left(\\frac{1}{6}\\right)^{11} \\qquad \\mathrm{(D)} \\frac{5}{2}\\left(\\frac{1}{6}\\right)^{11} \\qquad \\mathrm{(E)} \\left(\\frac{1}{6}\\right)^{10}$", "description_html": "<p>Twelve fair dice are rolled. What is the probability that the product of the numbers on the top faces is prime?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)} \\left(\\frac{1}{12}\\right)^{12} \\qquad \\mathrm{(B)} \\left(\\frac{1}{6}\\right)^{12} \\qquad \\mathrm{(C)} 2\\left(\\frac{1}{6}\\right)^{11} \\qquad \\mathrm{(D)} \\frac{5}{2}\\left(\\frac{1}{6}\\right)^{11} \\qquad \\mathrm{(E)} \\left(\\frac{1}{6}\\right)^{10}</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": "2005 AMC 10B Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc10B_p13", "prev": "/problem/05_amc10B_p11"}}