Prove that, if `P(A//B)=P(A)` then
`P(A^(c )//B)=P(A^(c ))`.

Prove that P(A^C) = 1 - P(A)

Prove that P(A uu B) = P(A) + P(B) - P(A nn B)

Given that P(A//B)=0.8, P(B//A)=0.6 and P(A^(c ) cup B^(c ))=0.7 , find the value of P(A//B^(c )) .

Two events A and B are such that P(A)=(1)/(4), P(B//A)=(1)/(2) and P(A//B)=(1)/(4) , then the value of P(A^(c )//B^(c )) is -

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 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 .

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).

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

If A and B are two events such that P(A)=0.3 , P(B)=0.25 , P(AnnB)=0.2 , then P(((A^(C ))/(B^(C )))^(C )) is equal to