reserve E for non empty set;
reserve a for Element of E;
reserve A, B for Subset of E;
reserve Y for set;
reserve p for FinSequence;
reserve e, e1, e2 for Singleton of E;

theorem Th36:
  for E being finite non empty set, A,B being Event of E st 0 <
  prob(B) holds prob(A, B) = 1 - prob(B \ A) / prob(B)
proof
  let E be finite non empty set, A,B be Event of E;
  prob(B \ A) + prob(A /\ B) = ( prob(B) - prob(A /\ B) ) + prob(A /\ B)
  by Th23;
  then prob(A, B) = ( prob(B) - prob(B \ A) ) / prob(B);
  then
A1: prob(A, B) = prob(B) / prob(B) - prob(B \ A) / prob(B) by XCMPLX_1:120;
  assume 0 < prob(B);
  hence thesis by A1,XCMPLX_1:60;
end;
