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Originally Posted by grant hutchison
There's no choice of urns. There's a single urn, which contains an unspecified quantity of consecutively numbered balls - anything from 10 to a million. We blindly select a ball, and find it's number 7. This is more likely to occur if the urn contains a small number of balls than a large number of balls.
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No, because you don't know the size of the single urn. In order to properly predict which urn you have (which is the point of the whole exercise) you need to consider all possibilities for urns.
In the case of 7, there's a 1/7 chance of picking the 7 ball if n=7, 1/8 if n=8, 1/9 if n=9, etc. Add up all those possibilities, as n tends to infinity. It's a divergent series, which means your 1/7 chance is singularly unlikely: you will never be the last person in your species. The only ways to resolve this are to change the series by weighting the odds to get a convergent series or to accept that the species will never die.