Inclusion-exclusion principle for probabilities
= Inclusion-exclusion principle for probabilities
{title2=$P(A\cup B)=P(A)+P(B)-P(A\cap B)$}
For a finite family of <events>, the <probability> of their <union> is the alternating sum of their <intersection> <probabilities>, with the same pattern as the <inclusion-exclusion principle>. Expand the <indicator function> of the <union> and apply <linearity of expectation>; this does not require <independent events>.