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A simplified stochastic model for the fiber structure of paper is introduced. The packing density and optical thickness of the fiber network are derived analytically, and their dependence on fiber characteristics can be seen. We undertake a Monte Carlo simulation of light scattering that is based on geometrical optics, using a realization of the model, which gives packing densities and optical thicknesses well in accordance with those given by the stochastic model and the scattering quantities as functions of three angles.