A Bayesian Network based mathematical model has been used for modelling Extreme Programming software development process. The model is capable of predicting the expected finish time and the expected defect rate for each XP release. Therefore, it can be used to determine the success/failure of any XP Project. The model takes into account the effect of three XP practices, namely: Pair Programming, Test Driven Development and Onsite Customer practices. The model's predictions were validated against two case studies. Results show the precision of our model especially in Predicting the project finish time.