Several rule induction schemes generate hypotheses in the form of unordered rule sets. One important problem that has to be addressed when classifying examples with such hypotheses is how to deal with overlapping rules that predict different classes. Previous approaches to this problem calculate class probabilities based on the union of examples covered by the overlapping rules (as in CN2) or assumes rule independence (using naive Bayes). It is demonstrated that a significant improvement in accuracy can be obtained if class probabilities are calculated based on the intersection of the overlapping rules, or in case of an empty intersection, based on as few intersecting regions as possible.