$\text{Two dice are rolled simultaneously. The probabilty that the numbers on them are different is }$

  $n\left(S\right)=6^2=36 ( total number of possible outcomes when two dice are rolled simul\tan eously)$ 

$$\begin{gathered} \text{Suppose that E be the event of getting two different numbers on dice } \\ \text{n(E)=\hspace{0.17em}6×5 =30} \end{gathered}$$           

$\text{Therefore, the probability for the required event is P(E)=}\frac{30}{36}=\frac{5}{6}$