2023 AMC 8 Problem 12

The figure below shows a large unshaded circle with a number of smaller unshaded and shaded circles in its interior. What fraction of the interior of the large unshaded circle is shaded?

\textbf{(A)} \dfrac{1}{4} \qquad \textbf{(B)} \dfrac{11}{36} \qquad \textbf{(C)} \dfrac{1}{3} \qquad \textbf{(D)} \dfrac{19}{36} \qquad \textbf{(E)} \dfrac{5}{9}

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