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Home Math Background Probability Additivity rule and mutually exclusive events  
See also: Summation of Probabilities  
Additivity Rule
The most simple method to determine the probability of a union of events is to count the sample points of the compound set (provided that the individual probabilities are equal). Sample points which belong to both sets of the compound event are counted only once. If we naively tried to calculate the probability of the union by simply adding the probabilities of the original sets A and B, we would find that the sum of the probabilities of the sets A and B is greater than the probability of the union of A and B. The difference is given by the probability of the intersection of A and B. From these considerations the probability of the union of two events can be calculated as follows: P(A) + P (B) = P(A B) + P(A B), so the probability of the union of two events A and B is given by:
Mutually exclusive events:Events A and B are mutually exclusive events, if A B contains no sample points, i.e. A and B have no sample points in common. In that case, the probability of the union of mutually exclusive events is just the sum of their probabilities. P(A B) = P(A) + P(B)


Home Math Background Probability Additivity rule and mutually exclusive events 