Infants' sensitivity to transitional probabilities (TPs) supports language development by facilitating mapping high-TP (HTP) words to meaning, at least up to 18 months of age. Here we tested whether this HTP advantage holds as lexical development progresses, and infants become better at forming word--referent mappings. Two groups of 24-month-olds (N = 64 and all White, tested in the United States) first listened to Italian sentences containing HTP and low-TP (LTP) words. We then used HTP and LTP words, and sequences that violated these statistics, in a mapping task. Infants learned HTP and LTP words equally well. They also learned LTP violations as well as LTP words, but learned HTP words better than HTP violations. Thus, by 2 years of age sensitivity to TPs does not lead to an HTP advantage but rather to poor mapping of violations of HTP word forms.