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This letter deals with ray propagation in stochastic distributions of discrete scatterers having random shapes. The propagation medium is described by means of a semi-infinite percolating lattice and two different propagation models are considered. The propagation depth inside the medium is analytically estimated in terms of the probability that a ray reaches a prescribed level before being reflected back in the above empty half-plane. A comparison with Monte Carlo-like experiments validate the proposed solutions. Applications are in wireless communications, remote sensing, and radar engineering.