We test contrasting predictions of two recent models of probability judgment: the quantum probability model (Busemeyer et al., 2011) and the probability theory plus noise model (Costello & Watts, 2014). Both models assume that people estimate probability using formal processes that follow or subsume standard probability theory. The quantum probability model predicts people's estimates should agree with one set of probability theory identities, while the probability theory plus noise model predicts a specific pattern of violation of those identities. Experimental results show just the form of violation predicted by the probability theory plus noise model. These results suggest that people's probability judgments do not follow quantum probability: instead, they follow the rules of standard probability theory, with the systematic biases seen in those judgments due to the effects of random noise.