In the scenario, there are two versions of the gene for magical ability — the M version, which creates muggles, and the W version, which is needed for wizardry. But everyone gets two copies of the gene — one from each parent — and even a single M scuttles any hope for a magical career.

Only the lucky few with the genes WW will have magical ability. Those who are MW will be muggles, but there is still a chance for their children. If two muggles who are MW have a child, there is a one in four chance that the child will be WW — and able to cast spells. —Matthew Harper —Harry Potter and the genetics lesson (Forbes|MSNBC)

A diverting little speculation.