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

Show that for any sets A and B, A = ( A ∩ B ) ∪ ( A – B ) and A ∪ ( B – A ) = ( A ∪ B )

Is it true that for any sets A and B, P ( A ) ∪ P ( B ) = P ( A ∪ B ) ? Justify your answer.

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

Given two independent events A and B such that P(A) = 0.3 P(B) = 0.6 , Find (i) P(A and B) (ii) P(A and not B) (iii) P(A or B) (iv) P(neither A nor 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))

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