In recent times, we have witnessed an increasing concern by governments and intelligence agencies to deploy mass-surveillance systems that help them fight terrorism. Although a government may be perfectly legitimate to do so, it is questionable whether a preventive-surveillance state is rational and cost-effective. In this paper, we conduct a theoretical analysis of the cost of such surveillance systems. Our analysis starts with a fairly well-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 percentage of terrorists the agency wishes to capture. Our formulation is first illustrated by means of several simple albeit insightful examples of terrorist and innocent profiles. Then, we conduct an extensive experimental study from real-world socio-demographic data of jihadist terrorism in the U.K. and Spain, and provide insight into the rationality and cost-effectiveness of two countries with two of the biggest defense budgets in the world.