Supposing `P(A cap B)>0`, show that `P(B cap C|A)=P(B|A)P(C|A cap B)`.

If A and B are two events and P(B) ne 1 , prove that, P(A//B^(c ))=(P(A)-P(A cap B))/(1-P(B)) Hence, deduce that, P(A cap B) gt P(A) +P(B)-1 .

If P(A cap B)=5/13 , P(Acap B)^c =

If P(A)=(2)/(3), P(B)=(1)/(2), P(A cap B)=(1)/(6) , then find the value of P(A cap B) and P(A cup B)

In three sets, A,B, C, show that (A cap B)' = A' cup B' .

For any two events A and B, show that max {P(A),P(B)} le P(A cup B) le min{P(A) + P(B),1} Where A cup B, A cap B, max{P(A), P(B)} and min {P(A)+P(B),1} are the occurence of A and B, occurence of A and B both, maximum of P(A) and P(B): minimum of P(A) + P(B) and 1 respectively.

For any two sets A and B, prove that P(A cap B) = P(A) capP(B) where P(A) is the power set of A.

For any two events A and b prove that, P(A cap B ) le P(A) le P(A cup B ) le P(A) + P(B)

If P(A) = (3)/(4) and P(B) = (5)/(8), show that, ,(3)/(8)le P(A cap B ) le (5)/(8), Now if the value of P(A cap B) is taken to be (1)/(2) , calculate P(A^( c) cap B^( c)) .

For any three events A, B and C, prove that. P(A cup B cup C) = P(A) + P(B) + P( C)-P(Acap B) -P(BcapC) - P(CcapA) + P(Acap B cap C).

The probabilities of three events A,B,C are P(A) = 0.6, P(B) = 0.4 and P( C) = 0.5.If P(A cup B) = 0.8, P(A cap C) = 0.3 , P(A cap B cap C) = 0.2 and P(A cup Bcup C ) ge 0.85, show that, 0.2 leP(BcapC) le 0.35.