Pretty hen!
Is she a bit dirty, or the brown on her neck part of the natural color of her feathers?
Either way, from what I can see, I think she has the genes to produce white chicks with most roosters, probably with some black bits on the chicks as well (paint).
Then I think that explains the black chick. The hen probably has the genes to be black all over, with one copy of the Dominant White gene (turns black into white, but misses a few bits.)
So she would give the genes for black-all-over to every chick.
She would give Dominant White to half of her chicks (turning them white with bits of black), and not to the other half (so they look black all over.)
The grayish one is a bit puzzling. I wonder if the hen also has the blue gene? If she did, it would not really be obvious, because blue turns black into a gray shade, but then Dominant White turns it all white anyway.