A new, probabilistic approach is applied to the case of dense random packings of binary mixtures of spheres, assuming gapless packing. The model describes correctly the dependence of the porosity of the packing on mixture composition and size ratio for the disordered dense "phase" of the binary mixture. The volumes of the voids are calculated accurately by means of a Monte Carlo integration instead of being evaluated by kissing spheres. The results, in term of the porosity/sphere-fraction relationship, are compared with those of a previous model, also based on the gapless packing approximation.