Mutually Exclusive Events
Two or more events are called mutually exclusive if the occurrence of any one event excludes the remaining events from occurring. For example, if A and B are mutually exclusive events, P(A ∩ B) = 0. Consequently, for two events A and B:
P(A ∪ B) = P(A) + P(B) − P(A ∩ B) becomes
P(A ∪ B) = P(A) + P(B)
or generally for any number of events:
P(A ∪ B ∪ C ∪...) = P(A) + P(B) + P(C) + ...
P(A ∪ B) = P(A) + P(B)
or generally for any number of events:
P(A ∪ B ∪ C ∪...) = P(A) + P(B) + P(C) + ...