If two dice are rolled then the probability of getting both even or sum 10 is

E= both even

 T= sum =10

$E\cap T=\left\{\right(4,6),(6,4\left)\right\}$

$P(E\cup T)=\frac{9}{36}+\frac{3}{36}-\frac{2}{36}$

                    $=\frac{10}{36}$

                     $=\frac{5}{18}$        

The probability of getting both even or sum 10 is  $\frac{5}{18}$