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)`

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

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

MULTIPLICATION THEOREM OF PROBABILITY Statement : If A and B are two events of a random experiment and P(A)gt0 and P(B)gt0 then P(AcapB)=P(A)P((B)/(A))=P(B)P((A)/(B))

If A and B are two events of a sample space then P(A)-P(B)=

If probability of a certain event A is P(A) = x, then P'(A) is

Prove that A and B are independent events if and only if P((A)/(B))=P((A)/(B^(C)))

If A,B are mutually exclusive and P(AcupB)ne0 then p((A)/(AcupB))=(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))