Approximate solutions of probability of hit problems have been achieved by means of a simulation involving a masked oscilloscope and photocell for the target and samples from random noise generators for the system dispersions. The method is described in general and its possible application to other noise and statistical problems indicated. The statistical limitations on accuracy and computation rate, inherent in such a sampling method, are analyzed for an idealized probability of hit problem which may be used as a guide in choosing appropriate noise spectra for the mechanization of similar problems. Examples which illustrate two types of restrictions on the noise spectra arising in amplifier bandwidth and screen response are considered in detail and the statistical relationship between computation rate and accuracy determined for spectra shaped by some simple RC filters.