Chances are about even that Mary put down the apple. It is certain that Julius is gray. It is probably not the case that Lily is gray. There is little chance that if either 'Lily is gray' or 'Julius is gray' but not both then Antoine is hungry. It is highly unlikely that if 'Julius is gray' or 'Mary put down the apple' or both then Brian is white. There is a better than even chance that if either 'Julius is gray' or 'Mary put down the apple' but not both then Daniel grabbed the apple.
It is probably not the case that either 'Mary put down the apple' or 'Daniel grabbed the apple' but not both.
There is a very good chance that either 'Mary put down the apple' or 'Daniel grabbed the apple' but not both.
It is probably not the case that either 'Mary put down the apple' or 'Daniel grabbed 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
  0.5::factA.
  1.0::factB.
  0.25::factC.
  %hop1
  0.1::factX:-xor(factC,factB).
  0.05::factY:-or(factB,factA).
  0.6::factZ:-xor(factB,factA).

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

  query(conclusion).
  
Either 'Mary put down the apple' or 'Daniel grabbed the apple' but not both.