The probability that atleast one of the two events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, evaluate `P(barA)+P(ba

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The probability that atleast one of the two events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, evaluate `P(barA)+P(barB)`.


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Salim Ahmed Kawsar

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We know that, `AcupB` denotes the occurance of atleast one of A and B and `AcapB` denotes the occurance of both A and B, simuletanously.
Thus, `P(AcupB)=0.6and P(AcapB)=0.3`
Also, `P(AcupB)=P(A)+P(B)_P(AcapB)`
`rArr 0.6=P(A)_P(B)-0.3`
`rArr P(A)+P(B)=0.9`
`rArr [1-P(barA)]+[1-P(barB)]=0.9` `[becauseP(A)=1-P(barA)and P(B)=1-P(barB)]`
`rArr P(barA)+P(barB)=2-0.9=1.1`

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