Chances are slight that Bernhard is green. It is probable that Mary is in the bathroom. It is probably not the case that Gertrude is a cat. There is a better than even chance that if 'Bernhard is green and Mary is in the bathroom' then Daniel grabbed the milk. Chances are about even that if 'Mary is in the bathroom' or 'Gertrude is a cat' or both then John took the football. It is almost certain that if either 'Gertrude is a cat' or 'Mary is in the bathroom' but not both then Lily is a rhino.
Chances are about even that either 'John took the football' or 'Mary is in the bathroom' but not both.
Chances are about even that either 'John took the football' or 'Mary is in the bathroom' but not both.
It is highly unlikely that either 'John took the football' or 'Mary is in the bathroom' 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.
  0.7::factB.
  0.25::factC.
  %hop1
  0.6::factX:-and(factA,factB).
  0.5::factY:-or(factB,factC).
  0.95::factZ:-xor(factC,factB).

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

  query(conclusion).
  
Either 'John took the football' or 'Mary is in the bathroom' but not both.