Algebra of Events
In a random experiment, let S be the sample space. Let A ⊆ S and B ⊆ S be the events in S. We say that
(i) (A Ո B) is an event that occurs only when both A and B occurs.
(ii) (A U B) is an event that occurs when either one of A or B occurs.
(iii) is an event that occurs only when A doesn’t occur.
· A ∩ = ɸ
· A∪ = S
· If A, B are mutually exclusive events, then P (A ∪ B) = P(A) + P (B)
· P (Union of mutually exclusive events) = ∑( Probability of events)
If A and B are two events associated with a random experiment, then prove that
(i) P (A Ո ) = P (only A) = P (A) −P (A ∩ B)
(ii) P ( Ո B) = P(only B) = P (B ) −P (A ∩ B)
(i) By Distributive property of sets,
Therefore, the events A
Ո B and A Ո are mutually exclusive whose union is A.
(ii) By Distributive property of sets,
Therefore, the events A Ո B and Ո B are mutually exclusive whose union is B.
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