In this relationship between the insurer and the policy-holder, between a contract of guarantees and a remuneration (premium or contribution), the insurance company faces up to a risk that is straight connects the information asymmetry which exists between it and the policy-holder. In a recent paper, A. Cohen (2005) shows that adverse selection is present with young drivers because they have a lack of experience, results which agree with the findings of Chiappori and Salanié (2000). The study presented in this paper comes within the framework of this last work. There is the equally question on the pertinence of the links existing between the accidents and the choice of contract of the young drivers. Our study is new on two points: - It concerns 4 types of guarantees (but no two), that is nearer to the reality in comparison to using a bivariate model. - These data are recent. They concern the year 2004, after the implementation of new security measures at the circulation: automatic radars, more strict control of blood alcohol content and more severe punishment for infractions. In addition, this new environment has brought about a decline in mortality from car accidents. In this modelling, the characteristics that explain the accidents and the choice of guarantee are correlated. In this case, the autonomous estimation of the equation of accidents can include an endogenous bias. The individual characteristics of the young drivers that explain the guarantee choice, explain also positively the probability of accidents. The hypothesis of adverse selection is verified among the young drivers who choose a contract "all risks" with a variable deductible.