Table of Contents
The Multiplication Rule
The AND probability (joint probability) calculates the likelihood that two or more events all occur. For independent events, multiply individual probabilities. For dependent events, use conditional probability P(A) times P(B|A).
Joint probability is always less than or equal to either individual probability, since requiring both events to occur is more restrictive than requiring just one.
Formulas
Examples
| Scenario | Type | Result |
|---|---|---|
| Two coin heads | Independent | 0.25 |
| Two aces from deck | Dependent | 0.0045 |
| Roll 6 twice | Independent | 0.0278 |
Frequently Asked Questions
How to know if events are independent?
Events are independent if one occurring doesn't change the other's probability. Coin flips are independent. Drawing cards without replacement is dependent.
Can P(A AND B) exceed P(A)?
No. The joint probability never exceeds either individual probability since A AND B is a subset of both A and B.
What about three or more events?
For independent events: P(A AND B AND C) = P(A) × P(B) × P(C). For dependent events, use the chain rule of conditional probability.