Now, computing the ratio p(x 1 )/q (0) (x 1 ) gives a result much below 1, because from the viewpoint of the full model p, the trigram (the two dog) is very unlikely; in other words the ratio w 3 (dog|the two)/w 1 (dog) (and, in fact, already the ratio w 2 (dog|two)/w 1 (dog)) is very low.
with high probability, x 1 is rejected.