Recent experimental studies suggest that risk aversion is negatively related to cognitive ability. In this paper we report evidence that this relation might be spurious. We recruit a large subject pool drawn from the general Danish population for our experiment. By presenting subjects with choice tasks that vary the bias induced by random choices, we are able to generate both negative and positive correlations between risk aversion and cognitive ability. Structural estimation allowing for heterogeneity of noise yields no significant relation between risk aversion and cognitive ability. Our results suggest that cognitive ability is related to random decision making, rather than to risk preferences.