Probability Calculus Some useful rules derived from Kolgomorov Axioms for random variables: Marginal Probability (\(B_i \cap B_j = \emptyset, \sum_i B_i = \Omega\)): \[P(A) = \sum_i P(A, B_i)\] Conditional Probability \[P(A,B) = P(B|A) P(A) = P(A|B) P(B)\] Chain Rule \[P(A_1, A_2 \ldots A_n) = P(A_1) P(A_2 | A_1) \ldots P(A_n|A_1, A_2 \ldots A_{n-1})\] Bayes’s rule \[P(A|B,C) = \frac{P(B|A,C) P(A|