We doubt that Brian is white. It is probably the case that Lily is green. There is almost no chance that John discarded the apple. It is highly unlikely that if 'John discarded the apple' or 'Brian is white' or both then Gertrude is a cat. There is a better than even chance that if either 'Lily is green' or 'John discarded the apple' but not both then Greg is white. It is highly unlikely that if either 'John discarded the apple' or 'Brian is white' but not both then Mary took the football.
It is highly unlikely that either 'Greg is white' or 'John discarded the apple' but not both.
Chances are about even that either 'Greg is white' or 'John discarded the apple' but not both.
It is highly unlikely that either 'Greg is white' or 'John discarded the apple' but not both.

  and(A,B) :- A,B.
  or(A,B) :- A;B.
  nand(A,B) :- not(and(A,B)).
  nor(A,B) :- not(or(A,B)).
  xor(A,B) :- or(A,B), nand(A,B).

  %hop0
  0.2::factA.
  0.7::factB.
  0.02::factC.
  %hop1
  0.05::factX:-or(factC,factA).
  0.6::factY:-xor(factB,factC).
  0.05::factZ:-xor(factC,factA).

  %hop2
  conclusion:-xor(factY,factC).

  query(conclusion).
  
Either 'Greg is white' or 'John discarded the apple' but not both.