Application to probability

Formula. For events $A_1,\ldots,A_n$ in a probability space:
$$P\left(\bigcup_i A_i\right)=\sum_iP(A_i)-\sum_{i<j}P(A_i\cap A_j)+\cdots+(-1)^{n+1}P(A_1\cap\cdots\cap A_n).$$

Conclusion. The formula follows from the set version by dividing by $|\Omega|$ (or $P(\Omega)$).