Inclusion-Exclusion Formula

If we have $A_{1}, A_{2}$
- Then $P (A_{1} \cup A_{2}) = P (A_{1}) + P (A_{2}) - P (A_{1} \cap A_{2})$
If we have:
- $P (A_{1} \cup A_{2} \cup A_{3}) = P (A_{1}) + P (A_{2}) + P (A_{3}) - P (A_{1} \cap A_{2}) - P (A_{1} \cap A_{3}) - P (A_{2} \cap A_{3}) + P (A_{1} \cap A_{2} \cap A_{3})$
$P (⋃_{i = 1}^{k} A_{i}) = \sum_{i = 1}^{k} P (A_{i}) - \sum_{i < j} P (A_{i} \cap A_{j}) + \dots + (- 1)^{k - 1} P (A_{1} \cap \dots \cap A_{k})$