This paper presents a Bayesian model for assessing the risk of the position of a study program (SP) within an Integrated University (IU). The model is based on Bayes' theorem of conditional probability and is used to evaluate the probability of the SP's future position in the IU. The model was developed using the example of the Engineering Management (EM) study program at the Technical Faculty in Bor, Serbia, to assess its probability of being included in the future Integrated University of Belgrade (IUB). The results show that the EM program has a probability of over 99% of being part of the IUB with its current structure and new activities. The model is universal and can be applied to assess the posterior probability of any SP's position and risk assessment by varying the number and content of the evidence nodes $ e_i $. The paper discusses the importance of universities in the global academic ranking and the transformation of non-integrated universities into integrated universities. The Technical Faculty in Bor (TFB) has four study programs: Mining Engineering (MI), Metallurgical Engineering (METI), Technological Engineering (TI), and Engineering Management (EM). The challenge is that three of these programs are being developed in parallel with other faculties, which may lead to some programs not being included in the IUB, resulting in a loss of affiliation with the top 500 universities. The paper also discusses the attitudes of professors in the TFB, which are influenced by a traditional communist ideology, and the motivation of these professors, which is primarily based on basic needs such as wages and job security. The study aims to assess the risk and determine the position of the EM program within the future IUB. The results show that the EM program has a high probability of being included in the IUB due to its strong performance in research, teaching, and student engagement. The Bayesian model is used to update the probability of the EM program's inclusion in the IUB based on various evidence nodes, leading to a high posterior probability of over 99%. The study concludes that the EM program has a good position in the IUB and that maintaining and promoting this position requires the commitment of more members of the program to the activities within the evidence nodes.This paper presents a Bayesian model for assessing the risk of the position of a study program (SP) within an Integrated University (IU). The model is based on Bayes' theorem of conditional probability and is used to evaluate the probability of the SP's future position in the IU. The model was developed using the example of the Engineering Management (EM) study program at the Technical Faculty in Bor, Serbia, to assess its probability of being included in the future Integrated University of Belgrade (IUB). The results show that the EM program has a probability of over 99% of being part of the IUB with its current structure and new activities. The model is universal and can be applied to assess the posterior probability of any SP's position and risk assessment by varying the number and content of the evidence nodes $ e_i $. The paper discusses the importance of universities in the global academic ranking and the transformation of non-integrated universities into integrated universities. The Technical Faculty in Bor (TFB) has four study programs: Mining Engineering (MI), Metallurgical Engineering (METI), Technological Engineering (TI), and Engineering Management (EM). The challenge is that three of these programs are being developed in parallel with other faculties, which may lead to some programs not being included in the IUB, resulting in a loss of affiliation with the top 500 universities. The paper also discusses the attitudes of professors in the TFB, which are influenced by a traditional communist ideology, and the motivation of these professors, which is primarily based on basic needs such as wages and job security. The study aims to assess the risk and determine the position of the EM program within the future IUB. The results show that the EM program has a high probability of being included in the IUB due to its strong performance in research, teaching, and student engagement. The Bayesian model is used to update the probability of the EM program's inclusion in the IUB based on various evidence nodes, leading to a high posterior probability of over 99%. The study concludes that the EM program has a good position in the IUB and that maintaining and promoting this position requires the commitment of more members of the program to the activities within the evidence nodes.