We derive an equation for the existence probability Ep for general percolation problem using an analytical argument based on exponential-decay behaviour of spatial correlation function. It is shown that the finite-size scaling function is well approximated by the error function. The present argument explain why it is universal. We use Monte Carlo simulation to calculate Ep for polydisperse continuum percolation and find that mono- and polydisperse system have the same finite-size scaling function.
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