Naive Bayesian classifiers have been very successful in attribute-value representations. However, it is not clear how the decomposition of the probability distributions on attribute-value tuples underlying those classifiers can be applied in the case of structured individuals, for instance sets of tuples as in the multiple instance problem. This paper presents a decomposition of probability distributions on structured individuals. Several probability distributions over lists, sets, and multisets are considered. In particular, an alternative to the bitvector distribution over sets is introduced. Decomposition as proposed in this paper introduces features (properties of the individual) that can be used, as in 1BC, to estimate the most likely class of an individual given its description.