How a child's ethnicity is determined?

How a child's ethnicity is determined?

I was always told it went by what the father is, but some people go by which parent is the minority. My oldest is half Puerto Rican, therefore I check the hispanic box on papers. She acknowledges both races though. I have 3 other children who are half Caucasian, and because their complexion is so light I mark both boxes. And I have a cousin who's bi-racial son has straight blonde hair and blue eyes, and I think she marks both boxes also. Because if you looked at him there's no way you'd believe his biological mother was black. And my 3 look like they have light tans. Unless you get close you'd think they were white or italian. But this was a very good question to ask.