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In probability theory, two events A and B are independent if the occurrence of one event does not affect the probability of the other occurring. Mathematically, this is expressed as P(A ∩ B) = P(A) × P(B), or equivalently, P(A|B) = P(A) and P(B|A) = P(B). For example, flipping a coin and rolling a die are independent events because the outcome of the coin flip doesn’t influence what number appears on the die. Independence is a crucial concept because it simplifies probability calculations—when events are independent, we can multiply their individual probabilities to find the probability of both occurring together. However, it’s important not to confuse independence with mutual exclusivity; mutually exclusive events (which cannot occur simultaneously) are actually dependent, since knowing one occurred means the other definitely did not.