Bridging associative and normative theories of animal learning, I show that an associative system can behave as if performing probabilistic inference by using the function f(V) = 1 − e^−cV to transform associative strengths (V) into response probabilities. For example, using this function, an associative system can respond normatively to a compound stimulus AB, given previous separate experiences with the components A and B. The CR probability formulae that result from the proposed function have a normative interpretation in terms of statistical decision theory. The formulae also suggest a normative interpretation of stimulus generalization as a heuristic to infer whether different stimuli are likely to convey redundant or independent information about reinforcement. (PsycInfo Database Record (c) 2022 APA, all rights reserved)