We introduce a mathematical framework for black-box software testing of functional correctness, based on concepts from stochastic process theory. This framework supports the analysis of two important aspects of testing, namely: (i) coverage, probabilistic correctness and reliability modelling, and (ii) test case generation. Our model corrects some technical flaws found in previous models of probabilistic correctness found in the literature. It also provides insight into the design of new testing strategies, which can be more efficient than random testing.