Assume that Jar S contains just silver balls, whereas Jar R contains ninety percent silver balls and ten percent red balls.

Someone secretly and randomly picks a jar, with an equal chance of choosing either. This picker then takes N randomly selected balls from his chosen jar with replacement. If a ball is silver he keeps silent, whereas if a ball is red he says “red.”

You hear nothing. You make the straightforward calculation using Bayes’ rule to determine the new probability that the picker was drawing from Jar S.

But then you learn something. The red balls are bombs and if one had been picked it would have instantly exploded and killed you. Should learning that red balls are bombs influence your estimate of the probability that the picker was drawing from Jar S?

I’m currently writing a paper on how the Fermi paradox should cause us to update our beliefs about optimal existential risk strategies. This hypothetical is attempting to get at whether it matters if we assume that aliens would spread at the speed of light killing everything in their path.