Abstract-In this paper, we consider the problem of designing in-vehicle driver-assist systems that warn or override the driver to prevent collisions with a guaranteed probability. The probabilistic nature of the problem naturally arises from many sources of uncertainty, among which the behavior of the surrounding vehicles and the response of the driver to on-board warnings. We formulate this problem as a control problem for uncertain systems under probabilistic safety specifications and leverage the structure of the application domain to reach computationally efficient implementations. Simulations using a naturalistic data set show that the empirical probability of safety is always within 5% of the theoretical value in the case of direct driver override, validating our models and algorithm. In the case of on-board warnings, the empirical value is more conservative due primarily to driver's decelerating more strongly than requested. But in all cases, the empirical value is greater than or equal to the theoretical value, demonstrating a clear safety benefit.Note to Practitioners: Abstract-Statistics show that a large percentage of vehicle crash fatalities and injuries happen in the proximity of intersections and stop signs. Many automotive companies have already released automated braking systems that warn drivers and reduce speed when approaching an obstacle. A major problem with the design of such driver-assist systems is to guarantee the absence of collisions even in the presence of uncertainty. In this work we present an approach using a probabilistic model for human driving behavior. The advantage of a probabilistic model is that it allows to distinguish between possible and probable scenarios. In particular, for any desired safety level P , our method guarantees safety as long as surrounding vehicles do not use behaviors from the 1 − P probability tail of their behavior distribution. Leveraging the monotone structure of the system we obtain an efficient algorithm that can compute warnings and overrides online. Moreover, simulations on a naturalistic data set show that the resulting override is considerably less conservative than one obtained when driver behavior is modeled through bounded uncertainty. There are a number of simplifying assumption made in this work, which limit the application mainly to prevention of rear-end collisions. We plan to generalize the method in order to be able to cover more general collision scenarios.