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if Aand B are two independent events then prove that the probability

if Aand B are two independent events then prove that the probability

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Grade:12th pass

1 Answers

Viren Jindal
31 Points
6 years ago
.          ​Probability of occurence of at least one of A  or B is P(AUB) = P(A) + P(B) – P(A^B).   
As Events are independent, P(A^B) = P(A).P(B)
 
Substituting, 
P(AUB) = P(A) + P(B) – P(A).P(B)
             = P(A) + P(B)[ 1 – P(A)]
             = P(A) + P(B).P(A’)
             = 1 – P(A’) + P(B).P(A’)
             = 1 – P(A’)[ 1 – P(B)]
            = 1 – P(A’)P(B’)

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