Studies in perception have found that humans often behave in accordance with Bayesian principles, while studies in higher-level cognition tend to find the opposite. A key methodological difference is that perceptual studies typically focus on whether people weight sensory cues according to their precision (determined by sensory noise levels), while studies with cognitive tasks concentrate on explicit inverse inference from likelihoods to posteriors. Here, we investigate if lay-people spontaneously engage in precision weighting in three cognitive inference tasks that require combining prior information with new data. We peel the layers of the “intuitive Bayesian” by categorizing participants into four categories: (a) No appreciation for the need to consider both prior and data; (b) Consideration of both prior and data; (c) Appreciation of the need to weight the prior and data according to their precision; (d) Ability to explicitly distinguish the inverse probabilities and perform inferences from description (rather than experience). The results suggest that with a lenient coding criterion, 58% of the participants appreciated the need to consider both the prior and data, 25% appreciated the need to weight them with their precision, but only 12% correctly solved the tasks that required understanding of inverse probabilities. Hence, while many participants weigh the data against priors, as in perceptual studies, they seem to have difficulty with “unpacking” symbols into their real-world extensions, like frequencies and sample sizes, and understanding inverse probability. Regardless of other task differences, people thus have larger difficulty with aspects of Bayesian performance typically probed in “cognitive studies.” (PsycInfo Database Record (c) 2022 APA, all rights reserved)