Explain why Hermione is a wizard even though both of her parents were muggles.

Answer:

Her ancestors were wizards, even though her parents weren't, they still had some knowledge of being wizards and stuff. Atleast i think so

Explanation:

Muggle-borns inherit magic from a distant ancestor; they are descended from Squibs who have married Muggles and whose families had lost the knowledge of their wizarding legacy. ... So even "muggle-borns" have ancestors who were magical at one point. Hermione was born magical. And she's not a muggle, she's a muggle-born.