We have a $2$ dice with $2$ evens and $4$ odds on both dice. For the sum to be even, the $2$ rolls can be $2$ odds or $2$ evens.  Ways to roll $2$ odds: 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: Similarly, we have $2 * 2=4$ ways to obtain $2$ evens.  The 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) $\dfrac{2}{3}$ 