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Chair and Varshney have presented an optimal rule for global decisions in distributed sensing scenario using Bayesian theory. This rule combines the decisions from different sensors weighted by their respective probability of detection and false alarm. The reliability of the combined decision is shown to improve with increasing number of sensors. In this paper, we present an analytical model to estimate the least number of sensors required to achieve a desired reliability (measured in terms of probability of error) in the global decision. Estimation of the required number of scanning sensors is expected to help design of energy conservation algorithms in which only a few sensors out a large group need to scan at a time. Accuracy of this estimate is validated using a simulation model, consisting of a large number of sensors accessing the same frequency bands.