| Property of Probability Functions | |
|---|---|
| The complement of an event A (i.e. the event A not occurring) | $ \,P(A^c) = 1 - P(A)\, $ |
| The intersection of two independent events A and B | $ \,P(A \mbox{ and }B) = P(A \cap B) = P(A) P(B)\, $ |
| The union of two events A and B (i.e. either A or B occurring) | $ \,P(A \mbox{ or } B) = P(A) + P(B) - P(A \mbox{ and } B)\, $ |
| The union of two mutually exclusive events A and B | $ \,P(A \mbox{ or } B) = P(A \cup B)= P(A) + P(B)\, $ |
| Event A occurs given that event B has occurred | $ \,P(A \mid B) = \frac{P(A \cap B)}{P(B)}\, $ |
