Each square in a 3 \times 3 grid is randomly filled with one of the four gray-and-white tiles shown below on the right.
What is the probability that the tiling will contain a large gray diamond in one of the smaller 2 \times 2 grids? Below is an example of such tiling.
Answer Choices
A. \dfrac{1}{1024}
B. \dfrac{1}{256}
C. \dfrac{1}{64}
D. \dfrac{1}{16}
E. \dfrac{1}{4}