Example 1. A die is rolled. What is the probability that an even number of points will come up?
Solution. Let's introduce the notation: $A$ - an even number of points has fallen; $B_{k}$ - $k$ points have fallen ( $k=1,2,3,4,5,6$ ). Event $A$ means that at least one of the events: $B_{2}, B_{4}, B_{6}$ has occurred, i.e., $A=B_{2}+B_{4}+B_{6}$. Since the events $B_{2}, B_{4}, B_{6}$ are mutually exclusive, we can use formula $(1.8 .3)$ for $n=3$, considering that $P\left(B_{k}\right)=1 / 6(k=1,2,3,4,5,6)$:

$$
P(A)=P\left(B_{2}\right)+P\left(B_{4}\right)+P\left(B_{6}\right)=\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{1}{2}
$$

Remark. The same result is obtained directly using the formula $P(A)=\frac{m}{n}=\frac{3}{6}=\frac{1}{2}$.