Question

Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by $4$ or $6$

Answer 1

Clearly $n\left(S\right)=6\times 6=36$

Let $E$ be the event that the sum of the numbers on the two faces is divided by $4$ or $6$.

Then $E=\{(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),(6,6)\}$

$n\left(E\right)=14$.

Hence $p\left(E\right)=\frac{n\left(E\right)}{n\left(s\right)}=\frac{14}{36}=\frac{7}{18}$