Addition Law of Probability

Theorem
Let $\Pr$ be a probability measure on an event space $\Sigma$.

Let $A, B \in \Sigma$.

Then:
 * $\map \Pr {A \cup B} = \map \Pr A + \map \Pr B - \map \Pr {A \cap B}$

That is, the probability of either event occurring equals the sum of their individual probabilities less the probability of them both occurring.

This is known as the addition law of probability.

Also presented as
Some sources present this result as:


 * $\map \Pr {A \cup B} + \map \Pr {A \cap B} = \map \Pr A + \map \Pr B$

Also known as
This result is also known as the sum rule, but then so are other results in mathematics.