The conventional theory of organic coatings assumes that the volume density of pigment particles is uniform throughout the sample. The coating is then described in terms of the pigment volume concentration Π, which equals the volume of pigment divided by the volume of pigment and polymer. Voids form in the coating when the pigment particles are randomly dense-packed, which implies that Π exceeds the critical pigment volume concentration (Φ c or that Λ=Π/Φ c > 1. Due to fluctuations in the local density of pigment however, some regions in the coating may become randomly dense-packed even below Φ c. Hence, voids may form in the densely-packed islands even when Λ<1. Our model for void formation contains two fitting parameters: N o is the smallest number of pigment particles in a densely-packed cluster that may contain a void; C q is the coarseness of the polymer space-filling in the volume of the sample not occupied by pigment. When C q=0 and Π > 1, the polymer completely fills the interstitial volume and the void concentration vanishes. But when C q > 0, voids may form in the densely-packed regions of the coating even below Φ c. The coarseness parameter C q, depends on the sample preparation, on the properties of the pigment and polymer, and on the pigment volume concentration Π. For any nonzero C q we conclude that optical measurements will systematically underestimate Φ c. On the other hand, since the density of polymer is less than half the density of pigment, the peak in the mass density p(Π) of the coating will overestimate Φ c. Unless C q is abnormally large, the void percolation threshold value Φ v is larger than Φ c and is a decreasing function of the coarseness C q. The predictions of this simple model are in good agreement with experiment, and are relevant to the general class of random concentrated composites which include organic coatings, ceramic polymer slips, composite solid polymer electrodes and some forms of battery separators.