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

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 .

Let 0ltP (A)lt1, 0ltP(B) lt1 and P(A uu B)=P(A)+P(B)-P(A)*P(B) then (A) P(B//A)=P(B)-P(A) (B) P(A^(c)-B^(c))-P(A^(c))-P(B^(c)), (C) P(A uu B)^(c)=P(A^(c))*P(B^(c)) (D) P(A//B)=P(A)

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, 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

If A, B, C are three events associated with a random experiment, prove that P(A uu B uu C) = P(A) + P(B) + P(C) - P(A nn B) - P(A nn C) P(B nn C) + P (A nn B nn C)

If A, B, C are three events associated with a random experiment, prove that P(A uu B uu C) = P(A) + P(B) + P(C) - P(A nn B) - P(A nn C) P(B nn C) + P (A nn B nn C)

If A, B, C are three events associated with a random experiment, prove that P(A uu B uu C) = P(A) + P(B) + P(C) - P(A nn B) - P(A nn C) P(B nn C) + P (A nn B nn C)