I thought of a better way of explaining the invalidity of the argument. What would happen if, instead of inferring from our own presence in the cubicle, we tak

I thought of a better way of explaining the invalidity of the argument. What would happen if, instead of inferring from our own presence in the cubicle, we take an external role. Furthermore, instead of taking the probability that a randomly selected person exists in of the two sets, we look at the probability that /someone/ exists in one of the two sets. If doom soon occurred, then the probability of cubicles 1-10 being occupied is 100%; If doom soon occurred, then the probability of cubicles 11-100 being occupied is 0%; If doom late occurred, then the probability of cubicles 1-10 being occupied is 100%; If doom late occurred, then the probability of cubicles 11-100 being occupied is 100%; So given those two probabilities, we have a 100% chance of cubicles 1-10 being occupied and a 50% chance of cubicles 11-100 being occupied. In either scenario, the occupancy status of cubicles 1-10 is assured. So checking in cubicles 1-10 gives us no meaningful information about which of the two scenarios occurred. Checking in cubicles 11-100 on the other hand /would/ affect our results. The occupancy of cubicles 11-100 on the other hand would tell us exactly which scenario occured.