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If A and B are two independent events...

If A and B are two independent events, then the probability of occurrence of at least one of A and B is given by `1" "" "P` (A) P (B)

Text Solution

Verified by Experts

We have,
P(At least one of A and B ) = `P(AcupB)`
`=P(A)+P(B)-P(AcapB)=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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