It is almost certain that Brian is gray. There is a very good chance that John picked up the apple. It is almost certain that Julius is a frog. It is probably the case that if 'John picked up the apple and Brian is gray' then Jessica is a mouse. There is almost no chance that if either 'Julius is a frog' or 'Brian is gray' but not both then Greg is yellow. We doubt that if 'John picked up the apple and Julius is a frog' then Mary got the milk.
It is highly unlikely that either 'Jessica is a mouse' or 'Mary got the milk' but not both.
Chances are about even that either 'Jessica is a mouse' or 'Mary got the milk' but not both.
It is highly unlikely that either 'Jessica is a mouse' or 'Mary got the milk' 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
  0.95::factA.
  0.8::factB.
  0.95::factC.
  %hop1
  0.7::factX:-and(factB,factA).
  0.02::factY:-xor(factC,factA).
  0.2::factZ:-and(factB,factC).

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

  query(conclusion).
  
Either 'Jessica is a mouse' or 'Mary got the milk' but not both.