Planet formation models suggest that the small exoplanets that migrate from beyond the snowline of the protoplanetary disk likely contain water-ice-rich cores (similar to 50% by mass), also known as water worlds. While the observed radius valley of the Kepler planets is well explained by the atmospheric dichotomy of the rocky planets, precise measurements of the mass and radius of the transiting planets hint at the existence of these water worlds. However, observations cannot confirm the core compositions of those planets, owing to the degeneracy between the density of a bare water-ice-rich planet and the bulk density of a rocky planet with a thin atmosphere. We combine different formation models from the Genesis library with atmospheric escape models, such as photoevaporation and impact stripping, to simulate planetary systems consistent with the observed radius valley. We then explore the possibility of water worlds being present in the currently observed sample by comparing them with simulated planets in the mass-radius-orbital period space. We find that the migration models suggest greater than or similar to 10% and greater than or similar to 20% of the bare planets, i.e., planets without primordial H/He atmospheres, to be water-ice-rich around G- and M-type host stars, respectively, consistent with the mass-radius distributions of the observed planets. However, most of the water worlds are predicted to be outside a period of 10 days. A unique identification of water worlds through radial velocity and transmission spectroscopy is likely to be more successful when targeting such planets with longer orbital periods.