It is probable that Brian is gray. There is almost no chance that Emily is a sheep. It is impossible that Mary dropped the milk. We believe that if either 'Brian is gray' or 'Mary dropped the milk' but not both then Julius is a swan. Chances are slight that if either 'Mary dropped the milk' or 'Emily is a sheep' but not both then Greg is white. There is almost no chance that if 'Emily is a sheep' or 'Mary dropped the milk' or both then John discarded the apple.
Chances are about even that either 'John discarded the apple' or 'Julius is a swan' but not both.
Chances are about even that either 'John discarded the apple' or 'Julius is a swan' but not both.
It is highly unlikely that either 'John discarded the apple' or 'Julius is a swan' 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
  0.7::factA.
  0.02::factB.
  0.0::factC.
  %hop1
  0.75::factX:-xor(factA,factC).
  0.1::factY:-xor(factC,factB).
  0.02::factZ:-or(factB,factC).

  %hop2
  conclusion:-xor(factZ,factX).

  query(conclusion).
  
Either 'John discarded the apple' or 'Julius is a swan' but not both.