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We study a process algebra which combines both nondeterministic and probabilistic behavior in the style of Segala and Lynch's simple probabilistic automata. We consider strong bisimulation and observational equivalence, and provide complete axiomatizations for a language that includes parallel composition and (guarded) recursion. The presence of the parallel composition introduces various technical difficulties and some restrictions are necessary in order to achieve complete axiomatizations

Compositional Reasoning for Probabilistic Finite-State Behaviors