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Dynamic all-red extension (DARE) has recently attracted research interest as a nontraditional intersection collision-avoidance method, for which the prediction of red-light running (RLR) and its related hazardous situations is a crucial part. We propose a probabilistic framework to model and predict RLR hazards for DARE. The RLR hazard, which is quantified by a predictive encroachment time, has contributory factors, including the speed, distance, and car-following status of the violator and the empirical distribution of the entry time of conflict traffic. An offline data analysis procedure is developed to set the parameters for RLR hazard prediction. Online-wise, a 2-D normal model is developed to predict the vehicle's stop-go maneuver based on speeds at advanced detectors and the car-following status. Additionally, unlike most prediction models that are designed to minimize mean errors, our model identifies two types of errors, namely, the false alarm and a missed report. The capability of distinguishing these two types of errors is crucial to the effectiveness of dynamic operations. To quantify the tradeoff between these two types of errors in DARE, a system operating characteristic (SOC) function is then defined. Effectiveness of the proposed model and its prediction algorithm is demonstrated using data collected from a field intersection. At a false-alarm rate of less than 5% (or equivalently about one false trigger per 8 h), the algorithm reached a correct detection rate of over 70% to more than 80%. Performance evaluation results showed that the proposed DARE framework can effectively predict the RLR hazards.