well, I think we did wrong.
at least I can be sure if 3 ducks, it's not 1/2
it's 3/4 for 3 ducks.
the first 2 ducks' angle could be 0 - 180, average 90.
so the third one has possibility of (360-90)/360 to fall into half circle for all 3 ducks.
kind of believe the answer is 1/2 (for 4 ducks), but do not know how to calculate for now.