In this paper we numerically study the probability Pac of the occurrence of car accidents in the extended Nagel–Schreckenberg (NS) model in the case of mixture of fast (Vmax1=5) and slow vehicles (Vmax2=1) by taking also to the risky overtaking of fast vehicles. In comparison with previous existing models, we find that accidents can occur in the free traffic phase and/or congested one depending on the overtaking rate of fast vehicles. The effect of evacuation of damaged vehicles from the road with probabilities Pevf and Pevs of fast and slow vehicles respectively on the traffic flow behavior is also computed. •Realistic car accident model.•Risky overtaking of fast vehicles.•Occurrence of accident even in free flow traffic.