We report the results of self-consistent Monte Carlo simulations of the density distribution along the normal to the interface of the liquid-vapor interface of a dilute ternary alloy of Sn and Pb in Ga. The results of the simulations are in general agreement with those obtained from experimental studies reported by Li, Yang, and Rice [Phys. Rev. B 65, 224202 (2002)], with some quantitative discrepancies. In particular, (i) the calculations reproduce the positions and relative amplitudes of the density strata in the liquid-vapor interface. The amplitudes of the density oscillations are overestimated by the simulations, which we attribute to residual inaccuracies in the pseudopotential employed and the limited size of the simulation sample. (ii) The calculations predict, and the experiments show, that at low temperature the excess Pb in the interface forms a complete monolayer that is the outermost layer of the liquid-vapor interface of the ternary alloy. (iii) The calculations predict, in agreement with inference from experiment, that when a complete Pb monolayer occupies the outermost layer of the interface, the excess Sn in the interface segregates in the second outermost layer. (iv) The calculations predict, in agreement with inference from experiment, that when a partial Pb monolayer occupies the outermost layer of the interface, the excess Sn in the interface is distributed between the outermost and second layers, and that the quasi-two-dimensional liquids of Sn and Pb in the outermost layer are immiscible. © 2005 The American Physical Society.