Chain Rule

We can compute probabilities using a chain rule as follows:

P(A ∧ B ∧ C) = P(A | B ∧ C) * P(B | C) * P(C)

If some conditions C₁ ∧ ... ∧ C_n are independent of other conditions U, we will have:

P(A | C₁ ∧ ... ∧ C_n ∧ U) = P(A | C₁ ∧ ... ∧ C_n)

This allows a conditional probability to be computed more easily from smaller tables using the chain rule.