Let ( be a partition of a sample space and suppose that each of has nonzero probability. Let A be any event associated with S,then
we know that P(S/F) =1
P(E U E'|F)=1 since EUE' =S
P(E/F) +P(E'/F) =1 since E and E' are disjoint events
P(E'/F) = 1- P(E/F)
P(EUF/G) ==
= +-
= P (E|G) + P (F|G) – P ((E ∩ F)|G)