1.

A, B, C किसी यादृच्छिक प्रयोग के संगत तीन घटनाएँ है तो सिद्ध कीजिए- `P(AuuBuuC)=P(A)+P(B)+P(C)-P(AnnB)-P(AnnC)-P(BnnC)+P(AnnBnnC)`

Answer» माना `E=BuuC`
`P(AuuBuuC)=P(AuuE)=P(A)+P(E)-P(AnnE)" "......(i)`
`P(E)=P(BuuC)=P(B)+P(C)-P(BnnC)" "......(ii)`
`AnnE=Ann(BuuC)=(AnnB)uu(AnnC)`
`impliesP(AnnE)=P(AnnB)+P(AnnC)-P[(AnnB)nn(AnnC)]`
`=P(AnnB)+P(AnnC)-P(AnnBnnC)" "......(iii)`
समीकरण (i), (ii), (iii) से
`P(AuuBuuC)=P(A)+P(B)+P(C)-P(AnnB)-P(AnnC)-P(BnnC)+P(AnnBnnC)`


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