2009 Pascal Problem 21

Alice rolls a standard 6-sided die. Bob rolls a second standard 6-sided die. Alice wins if the values shown differ by 1. What is the probability that Alice wins?

\textbf{(A)}\ \frac{1}{3}\quad \textbf{(B)}\ \frac{2}{9}\quad \textbf{(C)}\ \frac{5}{18}\quad \textbf{(D)}\ \frac{1}{6}\quad \textbf{(E)}\ \frac{5}{36}

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.