It also strikes me that the Carter hypothesis assumes that there must be a finite number of humans born a priori. In the version we're talking about here, it also assumes that there are only two options, the small urn and the big one. Even if we limited ourselves to a finite number of humans, why just these two choices? What happens to the odds if you have a billion urns, with a number of balls ranging from one to a billion? What if you have a trillion urns? Sure, by Bayesian reasoning, drawing number 7 means that the probability you drew it from the urn with 10 balls is greater than the probability you drew it from the urn with a million balls. But the overall probability that it was from a small urn goes steadily down as you increase the number of urns. And how do you know when to stop adding urns, unless you make an arbitrary decision ahead of time?