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Wireless sensor networks (WSNs) are being used in many applications in order to gather sensitive information and forward it to an analysis center. Since a WSN consists of resource- impoverished sensor nodes, the packet forwarding process should be energy efficient. Therefore, resource limitations should be taken into consideration when designing a WSN infrastructure. This paper proposes a random routing strategy for WSNs. The approach relies on the flooding technique, which has the advantage to possess minimal routing overhead (in the sense that no routing table information is exchanged) and maximal delivery rate. We introduce an enhancement that allows reducing energy consumption and extending network lifetime by randomly forwarding packets at every node. The forward probability is a decreasing function of the number of hops made by the packet. An analytical model is developed in order to illustrate the functionalities of the proposed strategy. Finally, simulations are conducted to assess the performance of the probabilistic routing protocols.