The following are axioms of probability on which probability theory is based on:
- 0 <= P(A) <= 1, where A is any event
- If an event is impossible: P(A) =0
- If an event is certain: P(A) =1
- P(A) = (number of favorable cases)/ (number of possible cases)
- P(S)=1, where S is the sample space
- P(not A) = P(A’) = 1 - P(A)
- P(A∪B) = P(A)+P(B), where A and B are mutually exclusive events
From the above axioms, the following formula can be derived:
P(A∪B) = P(A)+P(B)-P(A∩B), where A and B are not mutually exclusive events