Chances are about even that Bernhard is gray. It is improbable that Daniel dropped the milk. We doubt that Julius is yellow. It is likely that if 'Daniel dropped the milk' or 'Julius is yellow' or both then Bill went to the kitchen. It is impossible that if 'Bernhard is gray' or 'Julius is yellow' or both then Sandra took the apple. It is likely that if 'Daniel dropped the milk and Julius is yellow' then Gertrude is a sheep.
It is impossible that 'Daniel dropped the milk and Sandra took the apple'.
It is impossible that 'Daniel dropped the milk and Sandra took the apple'.
There is a very good chance that 'Daniel dropped the milk and Sandra took the apple'.

  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.
  0.1::factB.
  0.2::factC.
  %hop1
  0.7::factX:-or(factB,factC).
  0.0::factY:-or(factA,factC).
  0.7::factZ:-and(factB,factC).

  %hop2
  conclusion:-and(factB,factY).

  query(conclusion).
  
'Daniel dropped the milk and Sandra took the apple'.