How The F is Hermione A Witch?

Lily is muggle-born because of her parentage which are both muggles. How could two muggles unbelievably produce a magical child? My theory would be because they are descended from Squibs who married muggles, then their families lost the knowledge of their wizarding family. So the magic that skipped the squibs may have resurfaced in their great great grandchildren who became muggle-borns.

One can be a half-blood if a witch or wizard has at least one wizarding parent but at least one Muggle parent or grandparent, much similar to the case of Harry’s children, they are considered half-bloods because of Harry’s parentage: pure-blood father, Muggle-born mother.

Also there is this Dagworth-Granger, Hector(HB9) whom Proffessor Slughorn asked Hermione if she is related. Prof. Slughorn asked Hermione if she was related to Dagworth-Granger, she replied that she did not believe so, since she was Muggle-born. However, It is possible that Dagworth-Granger is a Squib and would have lost all knowledge of magic from their family.