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The concept of potential outcome types is one of the fundamental components of causal inference. However, even in randomized experiments, assumptions on the data generating process, such as monotonicity, are required to evaluate the probabilities of the potential outcome types. To solve the problem without such assumptions in experimental studies, a novel identification condition based on proxy covariate information is proposed in this paper. In addition, the estimation problem of the probabilities of the potential outcome types reduces to that of singular models when they are identifiable through the proposed condition. Thus, they cannot be evaluated by standard statistical estimation methods. To overcome this difficulty, new plug-in estimators of these probabilities are presented, and the asymptotic normality of the proposed estimators is shown.