P(A∩B) = P(A) × P(B|A) = P(B) × P(A|B). For independent events: P(A∩B) = P(A) × P(B). Events A and B are independent if: P(A|B) = P(A) or P(B|A) = P(B). Mutually exclusive vs independent: ME means P(A∩B)=0, independent means P(A∩B)=P(A)P(B).
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