There is almost no chance that Bernhard is yellow. There is almost no chance that Gertrude is a cat. It is probably the case that John went to the garden. It is probable that if 'Gertrude is a cat and John went to the garden' then Jessica is a sheep. It is impossible that if 'John went to the garden and Bernhard is yellow' then Julius is gray. There is a very good chance that if 'Bernhard is yellow' or 'John went to the garden' or both then Lily is a frog.
It is highly unlikely that either 'Bernhard is yellow' or 'Gertrude is a cat' but not both.
It is highly unlikely that either 'Bernhard is yellow' or 'Gertrude is a cat' but not both.
Chances are about even that either 'Bernhard is yellow' or 'Gertrude is a cat' 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
  0.02::factA.
  0.02::factB.
  0.7::factC.
  %hop1
  0.7::factX:-and(factB,factC).
  0.0::factY:-and(factC,factA).
  0.8::factZ:-or(factA,factC).

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

  query(conclusion).
  
Either 'Bernhard is yellow' or 'Gertrude is a cat' but not both.