Laws

Addition Law

Bayes’ Theorem

Suppose and are two events.

Can only be applied when:

• The sample space is partitioned into a set of mutually exclusive events: .
• is to be calculated
• At least one of the two sets of possibilities should be given:
  • and

Multiplication theorem

Law of total probability

Relates marginal probablities to conditiional probablities.

Suppose the sample space is partitioned into a countably infinite set of mutually exclusive events: . Then, for an event :

Joint Probability

Probability of 2 or more events occuring simultaneously.

Note

For discrete random variables, the marginal probability can be calculated by summing over the joint probability distribution:

For continuous random variables: