pigment

Can two fair skinned people produce a black child?

Nope.

Long version: there are at least 7 or 8 genes that control skin color. I believe that with most, if not all, dark is dominant to light, but I’m not sure of that. Even if light were dominant and dark were recessive, you’d need to have parents with the same recessive allele at, say, 5 or so loci, then combine those alleles in the kid. In that case, it would merely be wildly improbably.

So you’re saying the reverse is probable? That two blacks can have a fairskinned child? Or am I reading your math wrong?

If the darker genes are dominant, (Someone please confirm that they are) then yes it is definitely possible. Both black parents could be carriers for the recessive lighter genes but still be black. If the two recessive genes (overly simplified since we are not dealing with pea pods) end up in the child, then the child will be white.
Also, I knew an albino child who had two black parents. One could tell his parents were black because of his hair (even though it was blonde) and his facial features.

Sorry, I was answering barfly, not the OP.

To the OP.
I do not think it is possible. Not if the darker genes are dominant.

From Textbook of Human Genetics, by Max Levitan

Recent genetic discoveries notwithstanding, I think this is an old legend about “octaroons.”
My late grandfather once told me the most crackpot racist story I ever heard, about these octaroons. According to his story, 2 parents who each have as little as 1/8th black heritage and look entirely caucasian can produce a completely black child. I think this was a bunch of racist propaganda dating back to the Civil War, to discourage people from miscegenation.