What are the Axioms on which probability theory is based on?

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