Given a deterministic program, the probabilities of the program inputs, and a set of outputs, i.e., an output event, we will analyse the probability of the output event. We consider using established non-probabilistic analyses (either forward or backwards) that yield over-approximations of the program’s pre-image or image-relation, e.g., interval analyses. We assume a probability measure over the program input and present two techniques (one for forwards and one for backwards analyses) that both derive upper and lower probability bounds for the output events, and describe two case studies for the most involved technique, namely the forward technique.