Comment by jjk166

And it may be, but the important thing is we don't have priors that lead us to expect it to be fair.

We are not dealing with the tautologically true statement that we are assuming the 1/1000 estimate is correct and thus the odds are 1/1000 no matter what we measure. We are dealing with whether or not we can safely reject the hypothesis that the true odds are 1/1000 based on the actual observation of 1/12.

Billions of coins have been minted, and flipped a countless number of times, and we can do the physical analysis of coins such that we know the odds of a coin not being fair, without deliberate intervention to make them such, are astronomically low. As such no one is going to reject the hypothesis that a coin is fair based off of a small number of coin tosses. Hell even if you got 10 heads in a row, while the odds of that sequence is 1 in 1024, we would probably conclude it was luck rather than that the coin was flawed.

For spaceships on the other hand, those priors don't exist. We need to look at just the data from this particular test. The odds of a 1/1000 event occurring in the first 12 attempts is 1 in 84. For rejecting the hypothesis that a mass produced coin is fair, those odds aren't bad; but for rejecting the null hypothesis that the apollo capsules were just unlucky it's way over the reasonable threshold.