It is likely that Bernhard is gray. We doubt that Sandra dropped the milk. It is probably not the case that John discarded the apple. It is probable that if either 'Sandra dropped the milk' or 'Bernhard is gray' but not both then Mary went to the garden. Chances are about even that if either 'John discarded the apple' or 'Sandra dropped the milk' but not both then Greg is a rhino. It is unlikely that if either 'Sandra dropped the milk' or 'Bernhard is gray' but not both then Julius is white.
It is impossible that 'Bernhard is gray and Mary went to the garden'.
Chances are about even that 'Bernhard is gray and Mary went to the garden'.
It is impossible that 'Bernhard is gray and Mary went to the garden'.

  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.
  0.2::factB.
  0.25::factC.
  %hop1
  0.7::factX:-xor(factB,factA).
  0.5::factY:-xor(factC,factB).
  0.2::factZ:-xor(factB,factA).

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

  query(conclusion).
  
'Bernhard is gray and Mary went to the garden'.