Just to say - that the choice of RGB and CMYB is to some extent arbitrary. And three primary colours aren't enough to give all the colours we see.
That's because colour space is curved, and three primary colours can only define a triangular subset of it - that is unless you make some of the primary colours "outside" the range of colours we can see.
For instance this is the 1931 standard
And this is the sRGB standard
If you replot it on a colour disk like this, the lines become curved
As you can see, the CYMK standard gives you only a small part of the range of colours we can see with our eyes. That's why you'll never get a perfect reproduction of the colours in a Van Gogh masterpiece on your printer. But it is designed to work pretty well with the range of colours in photos, so they may print out fine.
Same also for computer displays. Really bright unsaturated colours particularly just don't reproduce well on computer displays and don't print out well either as most artists would probably testify.
WHY THERE ARE NO PERFECT PRIMARY COLOURS
The thing is - that yes - we do have only three colour receptors at the back of our eye (except for the few who are tetrachromats with four receptors, two red ones close in colour) - but the thing is - that there is no wavelength of light able to stimulate just one of those receptors.
All wavelengths stimulate all three receptors in differing amounts.
Indeed the "red" receptors are most responsive at yellow. But reds seem "red" because the other two colours have almost no response there. It is the nearest we have to a "pure" primary.
But in the blue direction then the "red" receptor trails off rather slowly - which is why "violet" in the spectrum has a tinge of red to it.
So - well a very long wavelength will trigger the "red" receptor mainly, it's not perfect but can be used as a "primary colour". But apart from that - a blue wavelength, for example, as you can see, triggers all three receptors. So is of no use as a "true primary".
Short of stimulating the receptors directly, electrically (or perhaps, shining laser light at individual receptors at the back of a human eye) - there is no way we can produce a true primary colour.
There is no way for our blue receptors to be stimulated by light without also stimulating the green and red receptors.
As a result there is no "perfect" choice of three primary colours. And even four, or five primary colours is not enough. Really you need the entire visual spectrum as primary colours to stimulate the eye with all possible colours it can see.
On the computer for instance, then yellows are always done as a mix of red and green light - so that limits the range of yellows you can use. They always have a little bit of white mixed in, so not pure yellows (though fine for sunlight).
When printing, the blue is a mix of cyan and magenta - and again many blues can't be made in that way.
So - actually many different sets of primary colours have been used historically for both mixing paints and for mixing lights. We happen to have standardized on Red, Green, and Blue for lights, and Cyan, Magenta and Yellow for printers. But artists don't generally use those as primary colours, or at least, not as their only primary colours.
Indeed many artists, like Van Gogh prefer to use paint that is unmixed, straight from the tube. Because mixed colours tend to be not quite so bright and unsaturated.
IMAGINARY AND IMPOSSIBLE COLOURS
As I just said, you can't stimulate, for instance, just the green receptor on its own, so we can't use it as a primary colour - but it is possible to see these "true primary colours" in some situations - if you can "exhaust" the other receptors.
For instance stare for a long time at a red square, then suddenly switch to a green square. Your red receptors have become exhausted, so you might see an "imaginary colour" - a green so green you can't see it in any other way.
Then also - there's another phenomenon that goes on, not mentioned yet - that you have. the Opponent process
When you see blue, then yellow is inhibited and vice versa. This probably happens at a later stage in the process after the light is received by the colour cones. There are three opposing "channels" red and green, blue and yellow, and black and white.
By shining pure blue light at one eye and pure yellow light at another, then you may find that you see an "impossible colour" that is simultaneously blue and yellow. Train yourself to see impossible colors
YUV ETC
The YUV standard on the computer is a compression standard, like mp3, based on human perception. See YUV
MIXING LIGHT OR MIXING PAINT
For anyone who doesn't know, paint works differently from light. With light, if you mix red and green light together you stimulate both the red and green receptors, which the eye perceives as a yellow. So it is additive, all the colours combine together to make the result you see.
With paints though, they are subtractive. Each pigment absorbs some colours and reflects others. When you mix pigments together, this absorbs more and more colours. So if you mix red, blue and yellow, or cyan magenta and yellow, or any mixture of paints widely separated in the spectrum you tend to get dark browns or black.
If you mix red, green and blue light, you get various tints of white.
The Pointillists however - they worked by mixing lights rather than mixing paints, by making their pictures out of many tiny dots of colour.
So you can use paint to mix additively as well, but this is unusual. See Pointillism
Here is a self portrait of Van Gogh, using the Pointillist technique.
And - paints also - they won't necessarily mix as expected. It is even worse than you would expect from the problem of reproducing primary colours. There is no way really to know, short of experience, what will happen when you mix two coloured paints together.
This video shows an example, a purply red that when mixed with a darkish blue gives a colour that is almost black already.
WHAT IS GOING ON HERE TECHNICALLY - WHY PAINTS MIX IN ECCENTRIC WAYS
Technically - the problem here is that paints have complex absorption and reflection spectra. And colours that look the same to a human eye, or almost the same, may have very different spectra. So you can't really tell, just by looking at the paint, how it is going to mix with another paint, you can only find out for sure by mixing them together to see what happens.
You could even, theoretically, have two paints that look pretty much identical to the eye, say blue, and then when you mix them together you get black (because they actually just reflect discrete wavelengths and one of them absorbs all the colours the other one reflects, so between them they absorb every colour).
Or, in theory, you could have two yellows, apparently identical, that mix together to make red - or another pair of yellows that mix to make green for that matter. In theory - I don't know if anyone has tried to deliberately make such paints :).
So - there really aren't any primary colours of paint. If you mix cyan with magenta then (usually, e.g. if you use printer's inks) you'll get a blue. But there are many other blues you can't get in that way. And then pigments behave in eccentric ways.
So, as an artist you just have to learn all the different pigments and how they mix together, basically.
I'm not an artist myself. But do remember mixing oil paints long ago and being surprised by some of the colours that resulted.
NO TRUE PRIMARIES THEN, JUST A STANDARD
So, RGB or CYMK are not really, in any sense, "true primaries".
This is just one choice of primaries - that we happen to have settled on. Obviously we needed a standard - so that we can have colour monitors that will work with any computer - and share digital photographs, and print out things on printers, and know that we will all get approximately the same colours.
The colours we use for our monitors, digital photos and printers - they work well for most movies, natural scenes and photographs as those images rarely need the brightest unsaturated colours.
E.g. how often do you see a pure unsaturated yellow? Even sunlight is mixed with white, not a pure yellow.
They don't work so well for reproducing some artist's paintings, however, especially if the artists tend to use bright unsaturated colours, e.g. Van Gogh is a good example - his work is one of the hardest challenges for colour reproduction because he was so keen on using bright coloured paint straight from the tube.
So - at some point someone had to make a decision (or some committee), what to use as the standard there. And they had good reasons for choosing those particular colours as primaries - but there were many other possible choices.