There is little chance that Daniel got the milk. It is unlikely that Bernhard is a frog. It is highly likely that John grabbed the apple. It is highly likely that if 'Daniel got the milk and John grabbed the apple' then Gertrude is a sheep. It is probable that if either 'Daniel got the milk' or 'John grabbed the apple' but not both then Mary went to the hallway. Chances are about even that if 'Bernhard is a frog' or 'Daniel got the milk' or both then Brian is white.
There is a very good chance that either 'Brian is white' or 'John grabbed the apple' but not both.
There is a very good chance that either 'Brian is white' or 'John grabbed the apple' but not both.
It is improbable that either 'Brian is white' or 'John 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
  0.1::factA.
  0.2::factB.
  0.9::factC.
  %hop1
  0.9::factX:-and(factA,factC).
  0.7::factY:-xor(factA,factC).
  0.5::factZ:-or(factB,factA).

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

  query(conclusion).
  
Either 'Brian is white' or 'John grabbed the apple' but not both.