Chances are slight that Mary went to the hallway. It is almost certain that Sandra got the football. We doubt that Greg is a lion. It is highly likely that if either 'Sandra got the football' or 'Greg is a lion' but not both then Lily is white. There is almost no chance that if 'Sandra got the football and Greg is a lion' then Gertrude is a sheep. Chances are about even that if 'Mary went to the hallway' or 'Sandra got the football' or both then John picked up the apple.
It is probable that either 'Mary went to the hallway' or 'Lily is white' but not both.
It is probable that either 'Mary went to the hallway' or 'Lily is white' but not both.
It is highly unlikely that either 'Mary went to the hallway' or 'Lily is white' 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
  0.1::factA.
  0.95::factB.
  0.2::factC.
  %hop1
  0.9::factX:-xor(factB,factC).
  0.02::factY:-and(factB,factC).
  0.5::factZ:-or(factA,factB).

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

  query(conclusion).
  
Either 'Mary went to the hallway' or 'Lily is white' but not both.