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We introduce different models where there is a mixture of uncertainty: probabilistic and fuzzy. The latter is modeled by fuzzy sets. We give various examples, arising from statistics. Then we discuss in more details the techniques used to investigate such problems. We focus on concepts such as : fuzzy probability, testing of inexact statistical hypotheses , distributions with fuzzy parameters, expected value with respect to a fuzzy probability, among others. Finally we explore the connections with aggregation of fuzzy sets based on inexact quantifiers.

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