People’s decisions and judgments are disproportionately swayed by improbable but extreme eventualities, such as terrorism, that come to mind easily. This article explores whether such availability biases can be reconciled with rational information processing by taking into account the fact that decision makers value their time and have limited cognitive resources. Our analysis suggests that to make optimal use of their finite time decision makers should overrepresent the most important potential consequences relative to less important, put potentially more probable, outcomes. To evaluate this account, we derive and test a model we call utility-weighted sampling. Utility-weighted sampling estimates the expected utility of potential actions by simulating their outcomes. Critically, outcomes with more extreme utilities have a higher probability of being simulated. We demonstrate that this model can explain not only people’s availability bias in judging the frequency of extreme events but also a wide range of cognitive biases in decisions from experience, decisions from description, and memory recall.