Additive Rule of Probability

Theorem

Given a probability space \((\Omega, \mathcal{F}, P)\), for any \(A, B \in \mathcal{F}\)

\[ P(A \cup B) = P(A) + P(B) - P(A \cap B).\]

This is just a simple consequence of this result, but is listed here as a different note since this is often separately called the additive rule of probability when working in the context of probability spaces.