I don't know who taught you this bullshit, but that is not the way it works in America. By your definition, a child that is the product of a white father and a black mother but looks like Lisa Bonet or Barack Obama would somehow be "white?" 
Please. Unless you are someone like the actress Jennifer Beals who can "pass" for white even though she is biracial, you can't get away with calling yourself white when your skin is darker than the average caucasian and your hair is tightly curled. Biracial people such as Halle Berry and Obama usually learn this reality early in life and therefore define themselves as black, lest they become very confused and hurt the first time they experience the racism they will surely face.
The whole concept of race is inherently bogus, but it is in essence defined in America by how you look and whether it has been determined that you have one drop of "black blood" in your ancestry.
BENNY BENNY BENNY...NOT SO STUPID...CUT BACK ON THE STUPID PILLS ALREADY...
You are talking about PHYSICAL APPEARANCE not race. RACE is an entirely different matter. As I have said RACE is not dependent on appearance...YES LENNY KRAVITZ is a WHITE MAN despite how he looks, MARIAH CAREY IS A BLACK WOMAN despite how she looks....NEITHER IS BI-RACIAL. There are many people walking around who are one race, but look entirely like another.
This STUPIDITY taught in america and american schools...that RACE IS DETERMINED BY HOW ONE LOOKS is ludicrous. Given that logic any male could dress himself up as a woman and be classified as a woman. Of course that is foolish, becasue physically and biologically he would be classified as a man and vice versa. Or how about a white person who tans is he/she now considered Black or maybe even putting on ProTan will classify a white person as Black, since in your mind race is dependent on appearance. So there must be a GREATER detemining factor in this classification, which then becomes GENETIC which then determines physical, psychological, biological features that classifies gender as a man or woman... and so the same with race. And that geneticv factor comes from the father (not of his choice) but based upon the genes which determine both gender and race.
Some of the most famous Black people who look white but are:
George Clooney
Frank Sinatra
Mariah Carey
Loni Anderson
Christina Aguillera
and quite a few others
