1&#x2F;36 is the probability that the detector is lying, and so when it says &quot;yes&quot; that means it&#x27;s a 1&#x2F;36 probability that the sun <i>hasn&#x27;t</i> gone nova, not the probability that it <i>could</i>.<p>$50 is only really any use if the sun hasn&#x27;t gone nova (cause otherwise we&#x27;re all dead), so therefore even if the odds are bad it&#x27;s still a good bet.<p>EDIT: Also, a penny just dropped after reading another of the answers. The odds against the sun having gone nova are incredibly mind-bogglingly high such that the the 1&#x2F;36 probability is negligible. So even if the probability that the machine is lying is small at 1&#x2F;36 it&#x27;s still far far far more likely than the sun having gone nova - which is the &quot;prior&quot; that the Bayesian is taking into account.<p>Another rub might also be that the frequentist&#x27;s significance (P-value) is not sufficient to take into account the astronomical scale of the Nova probability but IANAS so that&#x27;s just speculation.