“Stated differently, if you took 100 quarters and flipped each one of them 10 times, you could expect that one of the times you would have either 10 heads or 10 tails. If you do it with one quarter though, it is so unlikely that it will happen, that you can still conclude that it is weighted with reasonable certainty.”
I don’t think that is correct. If the percentage of weighted quarters in circulation is less than 1% (and I would guess it is whole lot less than that) and you picked up the coin at random, then it more likely that you just got lucky with your flipping than that the coin is weighted.
This is like the urban legend of the young man that shot himself after testing positive for AIDs. Only .04% of the tests produced false positives, but that number was still much larger than the percentage of people with AIDs in society. In other words there were more false positives with this test than true positives.