InterviewSolution
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InterviewSolution
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"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 |
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Answer» Correct Answer - 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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