Let EC denote the complement of an event E. Let E,F,G be pairwise independent events with P(G)>0 and P(E∩F∩G)=0.  Then PEC∩FC/G equals

We have,E∩F∩G=ϕPEc∩Fc/G =PEc∩Fc∩GP(G) =P(G)−P(E∩G)−P(G∩F)P(G) [From Venn diagram Ec∩Fc∩G=G−E∩G−F∩G=P(G)−P(E)P(G)−P(G)P(F)P(G)    ["' E' F' G are pairwise independent]=1−P(E)−P(F)=PEc−P(F)