We study the spatial distribution of trimethylamine-N-oxide (TMAO) and tert-butyl alcohol (TBA) molecules in aqueous solutions at low concentrations using molecular dynamics simulation, Voronoi-Delaunay method, and statistical cluster analysis. A comparison of these solutions with the systems of randomly distributed hard spheres is carried out. It is shown that TMAO molecules are generally distributed like random spheres. On the contrary, the distribution of TBA substantially differs from the random one, being the result of the self-association process in TBA solutions. Thus, using the methods of statistical geometry and systems of random spheres as a reference system, one can carry out a quantitative characterization of a global structure of a solution to describe general features of the spatial distribution of the solute molecules.