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In this paper, we study the minimum-latency broadcast scheduling problem in the probabilistic model. We establish an explicit relationship between the tolerated transmission-failure probability and the latency of the corresponding broadcast schedule. Such a tolerated transmission-failure probability is calculated in the strict sense that the failure to receive the message at any single node will lead to the entire broadcast failure and only if all nodes have successfully received the message do we consider it a success. We design a novel broadcast scheduling algorithm such that the broadcast latency is evaluated under such a strict definition of failure. The latency bound we derive is a strong result in the sense that our algorithm achieves a low broadcast latency under this rather strict broadcast-failure definition. Simulation results are also provided to justify our derived theoretical latency bound.