2023 AMC 8 Problem 23

Each square in a 3 \times 3 grid is randomly filled with one of the 4 shaded-and-unshaded tiles shown below on the right.

What is the probability that the tiling will contain a large shaded diamond in one of the smaller 2 \times 2 grids? Below is an example of such a tiling.

\textbf{(A)} \dfrac{1}{1024} \qquad \textbf{(B)} \dfrac{1}{256} \qquad \textbf{(C)} \dfrac{1}{64} \qquad \textbf{(D)} \dfrac{1}{16} \qquad \textbf{(E)} \dfrac{1}{4}

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