People overweigh small and underweigh large risks, resulting in probability weighting functions with an inverted S‐shape. This bias is stronger for affect‐rich outcomes: For two outcomes of the same monetary value, people are less sensitive to probability variation for affect‐rich than for affect‐poor outcomes (e.g., winning a $100 voucher toward a romantic dinner versus an electricity bill). In the current research, we investigated the interactive influence of affect and cognitive skills on probability weighting. Participants decided about buying insurance against the loss of an object, given various probabilities of loss. The description of the object was neutral, affect‐rich, or affect‐rich followed by an affective reappraisal task. The reappraisal task consisted of thinking about effective coping strategies and possible positive consequences of the loss. We also investigated the effect of numeracy on probability weighting. In particular, we investigated whether people have different affective responses to risks depending on their numerical abilities. Participants showed more overweighting of small probabilities for an affect‐rich than for a neutral outcome. This effect was mediated by fear. When participants were given the opportunity to reappraise the loss of the affect‐rich object, the effect disappeared. After reappraisal, participants' decisions were influenced by both fear and hope and were more in line with expectations based on normative models. The latter applied in particular to participants who had higher numeracy; they showed more emotional sensitivity to risks and assigned weights closer to linearity. Implications for the role of emotions and numeracy in risk communication are discussed. Copyright © 2013 John Wiley & Sons, Ltd.