No-shows are becoming a major problem in primary care facilities, creating additional costs for the facility while adversely affecting the quality of patient care. Accurately predicting no-shows plays an important role in the overbooking strategy. In this study, a hybrid probabilistic prediction framework based on the elastic net (EN) variable-selection methodology integrated with probabilistic Bayesian Belief Network (BBN) is proposed. The study predicts the "no-show probability of the patient(s)" using demographics, socioeconomic status, current appointment information, and appointment attendance history of the patient and the family. The proposed framework is validated using ten years of local pediatric clinic data. It is shown that this EN-based BBN framework is a comparable prediction methodology regarding the best approaches found in the literature. More importantly, this methodology provides novel information on the interrelations of predictors and the conditional probability of predicting "no-shows." The output of the model can be applied to the appointment scheduling system for a robust overbooking strategy.