The Bethe formula

An alternative to Neuberg, proposed by Henry Bethe, was discussed on BLML
The Bethe formula is:
PN = (Pn − 50) · n − 1

n + 1
· N + 1

N − 1
+ 50
If N > n the corrected percentages are in between those from Neuberg and the "manual method". The assumption made by Bethe is:
One conceptually attractive approach is to assume that the known group was drawn at random from the larger group. Since they are randomly drawn, all possible distributions within the larger set are equally likely. But the best guess is that the smaller set was equally distributed throughout the larger set.
We will not discuss the merits of this method here.