2015 AMC 10B Problem 11

Among the positive integers less than 100, each of whose digits is a prime number, one is selected at random. What is the probability that the selected number is prime?

\textbf{(A) } \dfrac{8}{99} \qquad\textbf{(B) } \dfrac{2}{5} \qquad\textbf{(C) } \dfrac{9}{20} \qquad\textbf{(D) } \dfrac{1}{2} \qquad\textbf{(E) } \dfrac{9}{16}

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