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I am curious, how does it makes sure that a name is fake? Even if its random, isn't there a high chance to generate a real name?

Yes but real names aren't guaranteed to be unique either, it's the combination of other fake information that matters.

Yes, but there is a 0% chance that the name it generates is someone who lives at that address with that phone number.

Your math does not checkout.

Ok, something like a 1 in 9,313,641,036,000,000,000,000 chance.