There is a better than even chance that John grabbed the apple. We doubt that Bernhard is green. It is highly unlikely that Greg is gray. There is little chance that if 'Greg is gray and Bernhard is green' then Julius is white. It is highly likely that if either 'Greg is gray' or 'John grabbed the apple' but not both then Sandra took the football. We doubt that if either 'John grabbed the apple' or 'Greg is gray' but not both then Lily is yellow.
It is improbable that either 'Lily is yellow' or 'Julius is white' but not both.
It is improbable that either 'Lily is yellow' or 'Julius is white' but not both.
There is a very good chance that either 'Lily is yellow' or 'Julius 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
  0.6::factA.
  0.2::factB.
  0.05::factC.
  %hop1
  0.1::factX:-and(factC,factB).
  0.9::factY:-xor(factC,factA).
  0.2::factZ:-xor(factA,factC).

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

  query(conclusion).
  
Either 'Lily is yellow' or 'Julius is white' but not both.