State and explain addition theorem of probability?

The addition theorem of probability states that for any two events A and B, the probability of either event A or event B occurring is given by: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). This formula accounts for the overlap between A and B (i.e., the intersection) by subtracting the probability of both events occurring together, ensuring that we don't double-count that overlap. If A and B are mutually exclusive events, the formula simplifies to P(A ∪ B) = P(A) + P(B) since P(A ∩ B) = 0.