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,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))

(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)

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

For any sets A and B, show that P ( A ∩ B ) = P ( A ) ∩ P ( B ) .

If P is a probability function, then show that for any two events A and B. P(AcapB)leP(A)leP(AcupB)leP(A)+P(B)

If A, B, C are any three events in an experiment then show that (i) P(A//B^(C)) = (P(A) - P(A nn B))/(1-P(B)) "if P"(B^(C)) gt 0 (ii) A sube B rArr P(A//C) le P(B//C) "if P(C)" gt 0 (iii) If A, B are mutually exclusive, then P(A//B^(C)) = (P(A))/(1-P(B)) "if P(B)" ne 1 (iv) If A, B are mutually exclusive and P(A uu B) ne 0 "then" P(A//A uu B) = (P(A))/(P(A) + P(B))

If A,B are two events, then show that P((A)/(B))P(B)+P((A)/(B^(C)))P(B^(C))=P(A).