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Chapter: 10th Mathematics : Statistics And Probability

Algebra of Events

In a random experiment, let S be the sample space. Let A ⊆ S and B ⊆ S be the events in S.

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.


Note:

·        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)

 

Thorem 1

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 (AB)

(ii) P ( Ո B) = P(only B) = P (B ) −P (AB)

Proof

(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.



Tags : Probability Probability
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