AMC 10 2021-fall-a Problem 9

When a certain unfair die is rolled, an even number is $3$ times as likely to appear as an odd number. The die is rolled twice. What is the probability that the sum of the numbers rolled is even? $\textbf{(A)}\ \frac{3}{8} \textbf{(B)}\ \frac{4}{9} \textbf{(C)}\ \frac{5}{9} \textbf{(D)}\ \frac{9}{16} \textbf{(E)}\ \frac{5}{8}$