For any two events A and B, shows that
`P(A^(C)capB^(C))=1" +"P(AcapB)-P(A)-P(B).`

For any two events A and B, show that, P(A uu B) = P(A) + P(B) - P(A nn B) .

For any two events A,B shows that P(AcapB)-P(A)P(B)=P(A^(C))P(B)-P(A^(C)capB) =P(A)P(B^(C))-P(AcapB^(C))

Foe any two events A and B prove that , P(A)geP(AcapB)geP(A)+P(B)-1

(i) If P is a probability function, show that for any two events A, B. P(AnnB) le P(A) le P(AuuB) le P(A)+P(B) (ii) For any two events A,B show that P(barAnnbarB)=1+P(AnnB)-P(A)-P(B)

For any three events A. B.' C show that P(AcupBcupC)=P(A)+P(B)+P(C)-P(AcapB)-P(BcapC)-P(CcapA)+P(AcapBcapC)

If A and B are any two events of a random experiment then show that (i) P(A^(C) nn B^(C)) = P(A^(C)) - P(B) "if A" nn B = phi (ii) P(A^(C)//B^(C)) = (1-P(A uu B))/(1-P(B)) "with P(A)" ne 0 and P(B) ne 1