We have a 2 die with 2 evens and 4 odds on both dies. For the sum to be even, the 2 rolls be 2 odds or 2 evens.  Ways to roll 2 odds (Case 1 ): The total number of ways to obtain 2 odds on 2 rolls is $4 * 4=16$, as there are 4 possible odds on the first roll and 4 possible odds on the second roll.  Ways to roll 2 evens (Case 2 ): Similarly, we have $2 * 2=4$ ways to obtain 2 evens. Probability is $\frac{20}{36}=\frac{5}{9}$ 
The faces of each of two fair dice are numbered $1$, $2$, $3$, $5$, $7$, and $8$. When the two dice are tossed, what is the probability that their sum will be an even number? (2019 AMC 8 Problems, Question \#18) 
A: $\dfrac{4}{9}$ 
B: $\dfrac{1}{2}$ 
C: $\dfrac{5}{9}$ 
D: $\dfrac{3}{5}$ 
E: $\dfrac{2}{3}$ 