| Rule | Formula | Description |
|---|
| Complement | P(A') = 1 - P(A) | Probability of NOT A occurring |
| Addition | P(A ∪ B) = P(A) + P(B) - P(A ∩ B) | Probability of A or B (or both) |
| Multiplication | P(A ∩ B) = P(A) × P(B|A) | Probability of both A and B |
| Conditional | P(A|B) = P(A ∩ B) / P(B) | Probability of A given B occurred |
| Independence | P(A ∩ B) = P(A) × P(B) | A and B do not affect each other |
| Bayes' Theorem | P(A|B) = P(B|A) × P(A) / P(B) | Reverse conditional probability |
| Total Probability | P(B) = Σ P(B|Aᵢ) × P(Aᵢ) | B over mutually exclusive events Aᵢ |