2022 AMC 10B Problem 12

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}?

\textbf{(A) } 2 \qquad \textbf{(B) } 3 \qquad \textbf{(C) } 4 \qquad \textbf{(D) } 5 \qquad \textbf{(E) } 6

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.