So there are two kinds of precision here: the precision of the mean probability given your current (incomplete) information, which can be arbitrarily high, and the precision with which you estimate the true answer, which is the width of the bell curve.
I’m not sure what you mean by the “true answer”. After all, in some sense the true probability is either 0 or 1 it’s just that we don’t know which.
That’s a good point. So I guess the second kind of precision doesn’t make sense in this case (like it would if the bell curve were over, say, the number of beans in a jar), and “precision” should only refer to “precision with which we can extract an average probability from our information,” which is very high.
I’m not sure what you mean by the “true answer”. After all, in some sense the true probability is either 0 or 1 it’s just that we don’t know which.
That’s a good point. So I guess the second kind of precision doesn’t make sense in this case (like it would if the bell curve were over, say, the number of beans in a jar), and “precision” should only refer to “precision with which we can extract an average probability from our information,” which is very high.