In recent times, we are witnessing an increasing concern by governments and intelligence agencies to deploy mass-surveillance systems that help them fight terrorism. In this paper, we conduct a formal analysis of the overall cost of such surveillance systems. Our analysis starts with a fairly-known result in statistics, namely, the false-positive paradox. We propose a quantitative measure of the total cost of a monitoring program, and study a detection system that is designed to minimize it, subject to a constraint in the number of terrorists the agency wishes to capture. In the absence of real, accurate behavioral models, we perform our analysis on the basis of several simple but insightful examples. With these examples, we illustrate the different parameters involved in the design of the detection system, and provide some indicative and representative figures of the cost of the monitoring program.