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))`

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

If A, B are two events, then show that (i) P((A)/(B))P(B)+P((A)/(B^(C )))P(B^(C ))=P(A) (ii) P(A^(c )|B^(c ))=(1-P(AuuB))/(1-P(B)),P(A) gt 0, P(B) ne 1 (iii) P(A//B^(C ))=(P(A)-P(AnnB))/(-P(B)),P(B^(C )) gt 0

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

If A,B,C are three events , Show that p( cup B cup C)= P(A)+P(B) + P( C) -P (A cap B) - P (B cap C) -P ( C cap A)+ P(A cap B cap C )

If A,B,C are three independent events of an experiment. Such that P(AcapB^(C)capC^(C))=(1)/(4) P(A^(C)capBcapC^(C))=(1)/(8),P(A^(C)capB^(C)capC^(C))=(1)/(4) then find P(A),P(B)and P( C).

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 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