Various sensor types, e.g., temperature, humidity, and acoustic, sense physical phenomena in different ways, and thus are expected to have different sensing models. Even for the same sensor type, the sensing model may need to be changed in different environments. Designing and testing a different coverage protocol for each sensing model is indeed a costly task. To address this challenging task, we propose a new probabilistic coverage protocol (denoted by PCP) that could employ different sensing models. We show that PCP works with the common disk sensing model as well as probabilistic sensing models, with minimal changes. We analyze the complexity of PCP and prove its correctness. In addition, we conduct an extensive simulation study of large-scale sensor networks to rigorously evaluate PCP and compare it against other deterministic and probabilistic protocols in the literature. Our simulation demonstrates that PCP is robust, and it can function correctly in presence of random node failures, inaccuracies in node locations, and imperfect time synchronization of nodes. Our comparisons with other protocols indicate that PCP outperforms them in several aspects, including number of activated sensors, total energy consumed, and network lifetime.