In probability theory, two events A and B are independent if the conditional probability of A given B equals the unconditional probability of A (or B has probability zero), which is logically equivalent to the product rule stating that the probability of their intersection equals the product of their individual probabilities; independence is symmetric and extends to mutual independence and pairwise independence for collections of more than two events, with pairwise independence being strictly weaker than mutual independence. The birthday principle is a derived combinatorial result showing that, for m items drawn independently and uniformly from n categories, the probability of at least one collision exceeds one half once m grows on the order of the square root of n, a phenomenon with direct application to hash-function collision analysis in computer science.
In probability theory, two events A and B are independent if the conditional probability of A given B equals the unconditional probability of A (or B has probability zero), which is logically equival…