Information processing involved in inference and decision-making has been explained from the viewpoint of the dual processes: intuitive system 1 and reflective system 2. The relationship between these two systems has been examined based on the difference between correct and incorrect answers in bias task. However, recently, another possible position, which questions the classification based on these answers, has been identified. For example, it is known that even if a participant provides an incorrect answer in a bias task, they may be able to detect a conflict between information about the correct and incorrect answers. In this study, participants were categorized according to their responses provided in the bias task and the presence or absence of conflict detection. The results showed that the functions of the two systems differ within the same answer. This result suggests that the classification based on the bias tasks is incomplete and that researchers need to consider a classification of participants based on the presence or absence of conflict detection.