The random sequential adsorption (RSA) approach was used to analyze adsorption of hard spheres at surfaces precovered with smaller sized particles. Numerical simulations were performed to determine the available surface function phi(l) of larger particles for various particle size ratios lambda = a(l)/a(s) and surface concentration of smaller particles theta(s). It was found that the numerical results were in a reasonable agreement with the formula Stemming from the scaled particle theory with the modification for the sphere/sphere geometry. Particle adsorption kinetics was also determined in terms of the RSA simulations. By extrapolating the theta(l) vs tau(-1/2) dependencies; the jamming concentrations of larger spheres theta(l)(infinity) were determined as a function of the initial smaller sphere concentration. It was found that theta(l)(infinity) were considerably reduced by the presence of smaller sized particles, especially for lambda much greater than 1. The pair correlation function g of larger particles in the jamming state was also determined, showing more short range ordering (at the same theta(l)) in comparison with monodisperse systems. The theoretical predictions stemming from our calculations suggest that the presence of trace amounts of very small particles may exert a decisive influence on adsorption of larger particles.