Global health interventions have a high probability of making a relatively small impact. Interventions that seek to eliminate or minimize existential threats often have a low probability of making an impact, and the probability of both the threat itself and the impact are hard to estimate; however, if they do make an impact, that impact will be enormous. Given these facts, which types of interventions should we focus on? I explore the difference that risk-aversion and risk-inclination, and ambiguity-aversion and ambiguity-seeking make to this question. Finally, I consider which of these attitudes we should adopt for purposes of ethics.