2020 Pascal Problem 17

Ben participates in a prize draw. He receives one prize that is equally likely to be worth \$5, \$10 or \$20. Jamie participates in a different prize draw. She receives one prize that is equally likely to be worth \$30 or \$40. What is the probability that the total value of their prizes is exactly \$50?

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

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.