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"If " P(AcupB)=P(AcapB)" for any two eve...

"If " `P(AcupB)=P(AcapB)`" for any two events A and B, then"`

A

`P(A)=P(B)`

B

`P(A)gtP(B)`

C

`P(A)ltP(B)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
(a) `"Given " P(AcupB)=P(AcapB)`
`P(A)+P(B)-P(AcapB)=P(AcapB)`
`rArr " "[P(A)-P(AcapB)]+[P(B)-P(AcapB)]=0`
`"But" " "P(A)-P(AcapB)ge=0`
`"and" " "P(B)-P(AcapB)ge=0" "[becauseP(AcapB)leP(A)or P(B)]`
`rArr " "P(A)-P(AcapB)=0`
`and " "P(B)-P(AcapB)=0`
`["since, sum of two non-negative numbers can be zero only when these numbers aree zero"]`
`rArr " "P(A)=P(AcapB)`
`and " "P(B)=P(AcapB)`
`therefore " "P(A)=P(B)`
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