{"status": "success", "data": {"description_md": "A pair of fair $6$-sided dice is rolled $n$ times. What is the least value of $n$ such that the probability that the sum of the numbers face up on a roll equals $7$ at least once is greater than $\\frac{1}{2}$?\n\n$\\textbf{(A) } 2 \\qquad \\textbf{(B) } 3 \\qquad \\textbf{(C) } 4 \\qquad \\textbf{(D) } 5 \\qquad \\textbf{(E) } 6$", "description_html": "<p>A pair of fair  <span class=\"katex--inline\">6</span> -sided dice is rolled  <span class=\"katex--inline\">n</span>  times. What is the least value of  <span class=\"katex--inline\">n</span>  such that the probability that the sum of the numbers face up on a roll equals  <span class=\"katex--inline\">7</span>  at least once is greater than  <span class=\"katex--inline\">\\frac{1}{2}</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 2 \\qquad \\textbf{(B) } 3 \\qquad \\textbf{(C) } 4 \\qquad \\textbf{(D) } 5 \\qquad \\textbf{(E) } 6</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": "2022 AMC 10B Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc10B_p13", "prev": "/problem/22_amc10B_p11"}}