The context of underwater sensor networks (UWSNs) presents special challenges for data transmission. For that context, we examine the merit of using a simple, stochastic transmission strategy based on the ALOHA protocol. The strategy uses a stochastic scheduling approach in which time is slotted, and each network node broadcasts according to some probability during each time slot. We present a closed-form solution to an objective function that guides the assignment of the broadcast probabilities with respect to overall network reliability. We propose an easily distributed heuristic based on local network density and evaluate our approach using numerical simulations. The evaluation results show that even without using explicit control signalling, our simple stochastic scheduling method performs well for data transmission in UWSNs.