In this paper, we perform a worst-case analysis of rule discovery. A rule is defined as a probabilistic constraint of true assignment to the class attribute of corresponding examples. In data mining, a rule can be considered as representing an important class of discovered patterns. We accomplish the aforementioned objective by extending a preliminary version of PAC learning, which represents a worst-case analysis for classification. Our analysis consists of two cases: the case in which we try to avoid finding a bad rule, and the case in which we try to avoid overlooking a good rule. Discussions on related works are also provided for PAC learning, multiple comparison, analysis of association rule discovery, and simultaneous reliability evaluation of a discovered rule.