Probability Chain Rule

The application of the Product Rule to a set of random variables via their joint probabilities

\mathrm{P}\left(X_1, \ldots, X_n\right) = & \text{ }\mathrm{P}\left(X_n \mid X_{n-1}, \ldots, X_1\right) \cdot \mathrm{P}\left(X_{n-1} \mid X_{n-2}, \ldots, X_1\right) \cdot \ldots \\ & \cdot \mathrm{P}\left(X_2 \mid X_1\right) \cdot \mathrm{P}\left(X_1\right) \end{align*}