The &quot;1&#x2F;36 chance&quot; and the &quot;negligible&quot; aren&#x27;t the corresponding&#x2F;analogous probabilities. 1&#x2F;36 is P(detector &quot;yes&quot; | not nova). The &quot;negligible&quot; is P(nova).<p>What we want to calculate is P(nova | detector &quot;yes&quot;). Using Bayes&#x27; rule it&#x27;s<p>P(nova | detector &quot;yes&quot;) = P(detector &quot;yes&quot; | nova) P(nova) &#x2F; (P(detector &quot;yes&quot; | nova) P(nova) + P(detector &quot;yes&quot; | not nova) P(not nova)) = 35&#x2F;36 * P_nova &#x2F; (35&#x2F;36 * P_nova + 1&#x2F;36 * (1-P_nova))<p>P(nova | detector &quot;yes&quot;) &gt; 0.5 if P_nova &gt; 1&#x2F;36.<p>This is also quite intuitive. Unless going nova is more likely than malfunctioning, you should bet on malfunctioning. This is very much like David Hume&#x27;s quote:<p>&quot;no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavors to establish.&quot; (test: would you say the same amount of &quot;holy crap! WTF!!&quot; if it turned out that the testimony was false, compared to if it turned out that the miraculous thing actually happened).<p>So: no detector &quot;yes&quot; is sufficient to establish the sun going nova, unless the detector saying &quot;yes&quot; be such, that it lying (1&#x2F;36) would be more miraculous, than the sun going nova.<p>It&#x27;s fascinating how precisely this can be formulated and how clear it is with probability theory.