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This paper considers a decision making problem of an autonomous car driving through the intersection with the presence of human-driving cars. A proactive collision avoidance system based on a learning-based MDP model is proposed in contrast to a reactive system. This approach allows to pose the question as an optimization problem. The proposed learning algorithm explicitly describes the interaction with the environment through a probabilistic transition model. The effectiveness of this concept is supported by a variety of simulations which include driving behaviors with Gaussian-distributed velocity, random actions and real human driving.