Probabilistic risk beliefs are key drivers of economic and health decisions, but people are not always certain about their beliefs. We study these "imprecise probabilities", also known as ambiguous beliefs. We show that imprecision is measurable separately from the levels of risk beliefs. People with higher levels of imprecision update their beliefs more in response to a randomized information treatment, and new information also causes changes in imprecision levels. We show that we can map our data onto both a standard Bayesian model and a version that is designed to handle imprecise probabilities; these models can match some features of our data but not all of them. Imprecise probabilities have important implications for our understanding of decisionmaking and for the design of programs intended to change people's minds.