How about all those wimpy “colors” like chartreuse or lavender or magenta? Those aren’t real, manly colors.
There is no straightforward answer, but the varieties have been shown here. Maybe the best lesson for your daughter is explaining how there can be more than one answer to some questions, and how to deal with that since she’ll probably run into the situation in school one day.
I picked the second option, but, unless you’re being totally pedantic, yes, they’re colors.
Next thing you know, that babysitter is going to be teaching Kiddo that 0.999… isn’t = 1.
I learned my colors the right way. Paranoiamakes it clear that Infra-red is black and ultraviolet is white and therefore black and white are both perceived colors and spectral colors. The babysitter has disobeyed The Computer and must now be terminated.
You, and several of the other posters in this thread, seem to be under the impression that there is some “scientific” definition of color, that differs from the everyday, colloquial meaning. It is notable that no-one says what that “scientific” definition is. There is a reason for that. It does not exist. Scientists use the word “color” just the same way as everybody else.
One idea that does seem to be in some people’s heads is that “scientifically” a color is only a “real” color if it matches some particular monochromatic wavelength of light. As bup points out in post#34, this is completely false. No color scientist holds such a view. People who say such things as that “scientifically” pink, or brown or black or white, or cerise, or whatever, are not colors are simply showing that they erroneously believe that the basic physics of the spectrum that they learned in high school is all there is to the science of color. Real color science does not try to legislate non-spectral colors out of existence, rather, it attempts to explain (amongst other things) how it is that people are able to experience so many of them, including ones (such as brown) that cannot be produced even by mixing various light wavelengths together.
Have you thought about getting a new babysitter?
I would assume that there are different professional groups who have different ways of categorizing colors. I don’t know what kind of background a color scientist would have, although my first guess would be physics, and I would guess that other groups who would have an interest in color would be photographers, graphic (and other) designers, psychologists, and biologists. The last two would be interested in the perceiving side of color, rather than the producing side.
For the strongest opinion that black is indeed a color, talk to a Klansman.
Well, that’s true, but pink is also a shade of red, and we consider all 4 colors.
So what are you going to tell her? How do adults tell their kids that another grown up is wrong, anyway? Hey, show her the wiki article for black, it says its a color 
I voted “yes” because paints come in black and white as well as all the other colours.
As above, technically speaking it’s complicated. Practically speaking, not only can I order black and white paint at the paint store, I can order innumerable shades of each. They’re colors.
you could write down “maybe” for grey. 
I do not think that physicists have had a whole lot of much of significance to contribute to our understanding of color since Newton discovered the spectrum back in the 17th century. The science that is concerned with trying to understand the nature of colors is an interdisciplinary field mainly at the intersection of neuroscience and psychology/cognitive science. I guess there are also chemists who are involved in stuff like creating new forms of dyes, but that is really quite a different mater, and more technology than science anyway.
As for your photographers, graphic designers, etc., well, they might reasonably have a professional interred in knowing something about color science, and some may know quite a bit about it, but that does not make them color scientists.