We test accuracies of the Percus-Yevick (PY) approximation for percolation thresholds and long-range correlated probability functions for continuum media of the adhesive sphere model. We clarify the universality of the continuum percolation of such a model and estimate the percolation thresholds for selected values of the adhesiveness parameter tau. We then calculate the pair-connectedness function and the two-point cluster function at percolation point and compare them with the analytical predictions by the PY approximation. We find that the PY approximation yields the pecolation points overestimated for tau >0.161 and underestimated for tau <0.161. The analytical calculations of the probability functions exhibit fairly good agreement with the Monte Carlo data for tau =0.161. However, for other values of tau, the analytical results show marked deviations from the Monte Carlo data. (C) 2001 American Institute of Physics.