2018 AMC 10A Problem 19

A number m is randomly selected from the set \{11,13,15,17,19\}, and a number n is randomly selected from \{1999,2000,2001,\ldots,2018\}. What is the probability that m^n has a units digit of 1?

\textbf{(A) } \frac{1}{5} \qquad \textbf{(B) } \frac{1}{4} \qquad \textbf{(C) } \frac{3}{10} \qquad \textbf{(D) } \frac{7}{20} \qquad \textbf{(E) } \frac{2}{5}

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