The usage of wireless sensor networks (WSNs) to monitor a region is an important functionality in defense and security applications. In these applications, a fundamental issue is to determine the minimum degree of coverage in the concerned region. The past researches focus on the binary disk sensing model, where sensors are assumed to be accurate in detecting targets within their sensing ranges. In this paper, we investigate the coverage problem under a more realistic model, the probabilistic sensing model, in which the probability of detection by a sensor decays with the distances. We generalize the coverage problem to the probabilistic sensing model and propose an algorithm to calculate the minimum degree of coverage. The accuracy of the proposed algorithm is verified via simulations.