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if And B are two independent events then provethat the probability

if And B are two independent  events then provethat the probability

Grade:12th pass

1 Answers

Arun
25763 Points
3 years ago
Dear Shreyansh 
 
you question is incomplete but I am solving it on my memory
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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