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In this paper, we examine the merit of a simple and lightweight stochastic transmission strategy based on the ALOHA protocol for underwater wireless sensor networks (UWSNs). We use a stochastic scheduling approach in which time is slotted, and each network component transmits according to some probability during each slot. We present objective functions for assigning the transmission probabilities that are aimed at optimizing network performance with respect to the overall network latency and the overall network reliability. We show that there is an easily distributed heuristic policy based on local network density that works well in practice. We also evaluate our approach using numerical simulations. The evaluation results show that even without using explicit control signaling, our lightweight stochastic scheduling method is effective for data transmission in underwater sensor networks.