If, by unfortunate means, Muggles do happen to observe the working of magic, the Ministry of Magic sends Obliviators to cast Memory Charms upon them, causing them to forget the event. Some Muggles are aware of the wizarding world.
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The WeasleysWe finish on a family who are technically quite pure-blood, but are deemed 'blood traitors' by various peers, and seem proud of it. It is, indeed, the Weasleys' compassion and morals that led to several members marrying half-bloods, Muggle-borns, etc.