2013 Pascal Problem 20

Sam rolls a fair four-sided die containing the numbers 1, 2, 3, and 4. Tyler rolls a fair six-sided die containing the numbers 1, 2, 3, 4, 5, and 6. What is the probability that Sam rolls a larger number than Tyler?

\textbf{(A)}\ \frac{1}{8}\quad \textbf{(B)}\ \frac{5}{12}\quad \textbf{(C)}\ \frac{3}{5}\quad \textbf{(D)}\ \frac{3}{4}\quad \textbf{(E)}\ \frac{1}{4}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.