Decision making often requires simultaneously learning about and combining evidence from various sources of information. However, when making inferences from these sources, humans show systematic biases that are often attributed to heuristics or limitations in cognitive processes. Here we use a combination of experimental and modelling approaches to reveal neural substrates of probabilistic inference and corresponding biases. We find systematic deviations from normative accounts of inference when alternative options are not equally rewarding; subjects' choice behaviour is biased towards the more rewarding option, whereas their inferences about individual cues show the opposite bias. Moreover, inference bias about combinations of cues depends on the number of cues. Using a biophysically plausible model, we link these biases to synaptic plasticity mechanisms modulated by reward expectation and attention. We demonstrate that inference relies on direct estimation of posteriors, not on combination of likelihoods and prior. Our work reveals novel mechanisms underlying cognitive biases and contributions of interactions between reward-dependent learning, decision making and attention to high-level reasoning.