Probability Axioms
Sample Space and Events
Probability Measure
The triple is a probability space.
Basic Properties
Inclusion-Exclusion
Conditional Probability
Multiplication Rule
Law of Total Probability
where is a partition of .
Bayes' Theorem
Examples
Example 1: Fair die: .
Example 2: Two dice: .
Example 3: Birthday problem:
Independent Events
Pairwise vs. Mutual Independence
Bonferroni's Inequality
Applications
- Risk assessment
- Medical testing
- Quality control
- Gambling odds
- Statistical inference