Automobile insurance is one of the main pillars of the entire insurance industry in the developed economies. Knowing as much as possible about the factors related to the accidents is an essential issue for the insurance companies so that they may improve their levels of efficiency. Therefore, in this paper we focus on studying the most relevant variables that help explain the registration of claims in the automobile insurance sector. For this purpose, we fit a probit model specification using a database from a Spanish insurance company. Our research points out the significance of certain variables, such as the policyholders' driving experience, their region of residence as well as their levels of insurance coverage, towards the likelihood of registering an insurance claim. However, probit analysis represents only one of the multiple perspectives which we can consider to examine the question of accidents and their reporting. Very briefly, we also discuss the utility of zero-inflated count data models to study the number of accidents declared by policyholders. Finally, we point out the possibilities that thinned models could offer for this type of research.