It is probable that Julius is a frog. There is little chance that Brian is yellow. There is a better than even chance that Mary took the milk. Chances are about even that if either 'Julius is a frog' or 'Brian is yellow' but not both then Gertrude is a sheep. It is improbable that if 'Brian is yellow and Mary took the milk' then Sandra left the milk. It is highly unlikely that if either 'Julius is a frog' or 'Brian is yellow' but not both then Antoine is thirsty.
It is highly unlikely that 'Brian is yellow and Julius is a frog'.
It is highly unlikely that 'Brian is yellow and Julius is a frog'.
It is likely that 'Brian is yellow and Julius is a frog'.

  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
  0.7::factA.
  0.1::factB.
  0.6::factC.
  %hop1
  0.5::factX:-xor(factA,factB).
  0.1::factY:-and(factB,factC).
  0.05::factZ:-xor(factA,factB).

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

  query(conclusion).
  
'Brian is yellow and Julius is a frog'.