Topics: Probability Measure - Probability


(theorem)

Let be the probability measure of an event . This probability measure has the following properties:

  1. If , then
  2. The probability measure is monotonic. That is:

Finite Additivity

(theorem)

Let , where (; disjoint). Then:

Finite Subadditivity

(theorem)

Let not necessarily disjoint. Then:

This property is also known as Boole’s inequality.

Inclusion-Exclusion Rule

(theorem)

Let not necessarily disjoint. Then: