Probabilistic Bipolar Abstract Argumentation Frameworks (prBAFs), combining the possibility of specifying supports between arguments with a probabilistic modeling of the uncertainty, are considered, and the complexity of the fundamentalproblem of computing extensions' probabilities is addressed.The most popular semantics of supports and extensions are considered, as well as different paradigms for defining the probabilistic encoding of the uncertainty.Interestingly, the presence of supports, which does not alter the complexity of verifying extensions in the deterministic case, is shown to introduce a new source of complexity in some probabilistic settings, for which tractable cases are also identified.