Product rule
Theorem taught in Random experiments and probability, part of Probability
Product rule
| Type | Theorem |
| Taught in | Random experiments and probability |
| Part | Probability |
| Questions using it | 1 |
If \mathbb{P}(A_1\cap\cdots\cap A_{n-1})>0, then
\mathbb{P}(A_1\cap\cdots\cap A_n) =\mathbb{P}(A_1)\,\mathbb{P}(A_2\mid A_1)\,\mathbb{P}(A_3\mid A_1\cap A_2)\cdots\mathbb{P}(A_n\mid A_1\cap\cdots\cap A_{n-1}).
Each factor is the definition of conditional probability, and the intermediate intersections cancel.
Used in
- Taught in Random experiments and probability, where the derivation and examples are.
- Also used in Joint distributions
- Questions that use it (1) — A point in a triangle (answer)
- All 17 questions on Random experiments and probability
See also
Conditional probability · Law of total probability · Sample space · Event · Probability measure · Properties of a probability · Equally likely outcomes · Four ways of counting draws