Katie Mosher: How exactly do muggleborns receive magical ability

J.K. Rowling: Muggle-borns will have a witch or wizard somewhere on their family tree, in some cases many, many generations back. The gene re-surfaces in some unexpected places.

http://www.accio-quote.org/articles/2007/0730-bloomsbury-chat.html

https://www.butajape.com/comic/young-adult-protagonist/