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Abstract: While sensing coverage reflects the surveillance quality provided by a wireless sensor network (WSN), network connectivity enables data gathered by sensors to reach a central node, called the sink. Given an initially uncovered field and as more and more sensors are continuously added to a WSN, the size of partial covered areas increases. At some point, the situation abruptly changes from small fragmented covered areas to a single large covered area. We call this abrupt change as the sensing-coverage phase transition (SCPT). Also, given an originally disconnected WSN and as more and more sensors are added, the number of connected components changes such that the WSN suddenly becomes connected at some point. We call this sudden change as the network-connectivity phase transition (NCPT). The nature of such phase transitions is a central topic in percolation theory of Boolean models. In this paper, we propose a probabilistic approach to compute the covered area fraction at critical percolation for both of the SCPT and NCPT problems. Because sensing coverage and network connectivity are not totally orthogonal, we also propose a model for percolation in WSNs, called correlated disk model, which provides a basis for solving the SCPT and NCPT problems together.