The paper considers the mixture of randomness and fuzziness in a binary tree classifier. This model of classification is based on fuzzy observations, the randomness of classes and the Bayes rule. In this work, we present a new upper bound on the probability of error in a binary tree classifier. The obtained error for fuzzy observations is compared with the case when observations are not fuzzy, as a difference of errors. Additionally, the obtained results are compared with the bound on the probability of error based on information energy of fuzzy events. For interior nodes of decision tree, the new bound is twice as precise as the bound based on information energy.