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We develop a general testing scenario for probabilistic processes, giving rise to two theories: probabilistic may testing and probabilistic must testing. These are applied to a simple probabilistic version of the process calculus CSP. We examine the algebraic theory of probabilistic testing, and show that many of the axioms of standard testing are no longer valid in our probabilistic setting; even for non-probabilistic CSP processes, the distinguishing power of probabilistic tests is muchdoi:10.1016/j.entcs.2007.02.013 fatcat:7ffmnzj7jfe6xcadstjovvb5kq