Chain rule (probability)

For random variables $A_i$ for $i \in \{1, 2, \ldots, n\}$ we have

$$\mathbb{P}[A_1, A_2, \ldots, A_k] = \prod_{k=1}^n \mathbb{P}[A_k \vert A_1, A_2, \ldots, A_{k-1}].$$

This follows from the definition of conditional probability.