It is impossible that Mary went to the garden. It is highly likely that Bernhard is white. There is little chance that Gertrude is a sheep. Chances are about even that if 'Gertrude is a sheep and Bernhard is white' then Jeff left the apple. We doubt that if either 'Bernhard is white' or 'Mary went to the garden' but not both then Lily is white. It is likely that if 'Gertrude is a sheep' or 'Mary went to the garden' or both then Julius is yellow.
Chances are about even that either 'Jeff left the apple' or 'Mary went to the garden' but not both.
It is highly unlikely that either 'Jeff left the apple' or 'Mary went to the garden' but not both.
Chances are about even that either 'Jeff left the apple' or 'Mary went to the garden' 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
  0.0::factA.
  0.9::factB.
  0.1::factC.
  %hop1
  0.5::factX:-and(factC,factB).
  0.2::factY:-xor(factB,factA).
  0.7::factZ:-or(factC,factA).

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

  query(conclusion).
  
Either 'Jeff left the apple' or 'Mary went to the garden' but not both.