Dropping out from STEM higher education is a severe global issue that needs action and solution, in Hungary the dropout rate is particularly high. Exploring the causes of early school leaving is a well-studied research topic of great interest. In this paper, we study the relationship between pre-enrollment achievement measures and indicators of first-year university performance, using Bayesian networks, based on the academic data of students of the mechanical engineering bachelors program at the Budapest University of Technology and Economics. Bayesian networks are having their renaissance, thanks to the high number of openly available software tools. We demonstrate the applicability of Bayesian networks in the educational domain, moreover, we also include a high-level but detailed description of the algorithms, which other similar papers usually lack. Although the models perform generally quite well, we also point out inconsistencies in the results and some limitations of the models.