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Considering event-driven clustered wireless sensor networks, a probabilistic approach for analyzing the network lifetime is presented when events occur randomly over the network field. To this end, we first model the packet transmission rate of the sensors, using the theory of coverage processes and Voronoi tessellation. Then, the probability of achieving a given lifetime by individual sensors is found. This probability is then used to study the cluster lifetime. In fact, we find an accurate approximation for the probability of achieving a desired lifetime by a cluster. Our proposed analysis includes the effect of packet generation model, random deployment of sensors, dynamic cluster head assignment, data compression, and energy consumption model at the sensors. The analysis is presented for event-driven networks, but it comprises time-driven networks as a special case. Computer simulations are used to verify the results of our analysis.