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The safety of the planned paths of autonomous cars with respect to the movement of other traffic participants is considered. Therefore, the stochastic occupancy of the road by other vehicles is predicted. The prediction considers uncertainties originating from the measurements and the possible behaviors of other traffic participants. In addition, the interaction of traffic participants, as well as the limitation of driving maneuvers due to the road geometry, is considered. The result of the presented approach is the probability of a crash for a specific trajectory of the autonomous car. The presented approach is efficient as most of the intensive computations are performed offline, which results in a lean online algorithm for real-time application.