From early childhood I learned that the primary colours (from which all others are mixed) are red, blue and yellow,
Red and blue make purple/violet, blue and yellow make green, yellow and red make green.
Yes and No!
It depends on which red, yellow or blue you choose. Pick the wrong ones and you end up with dull muddy colours, and that's why many artists say it's necessary to have a warm and a cool version of each primary colour in a paintbox.
Later on in physics lessons we were taught that the primary colours are red, blue and green.
But this is when mixing coloured light, and not when mixing paints.
White light comes from the sun and can be split into the colours of the rainbow by passing the light through a glass prism - or it can occur in nature as a ranbow when fine droplets of water/rain work in the same way as the glass. The visible colours in the rainbow are red, orange, yellow, green, blue and violet. The presence of "indigo" between is blue and violet is now not generally considered to be there. Can you see indigo in the photo?
Beams of coloured light can be obtained from coloured lamps or by covering a white light source (a torch) with coloured cellephane (sweet wrappers) and experiments will show that red, blue and green are indeed the primary colours of light, and that red and blue make magenta, blue and green make cyan, blue and red make yellow and red, blue and green together make white. These are the red/blue/green colours used in TV and computer screens.
Image from en.wikipedia.org/wiki/Green
So the primary colours in light are red, blue and green and the secondary colours are magenta, cyan and yellow.
If those colours sound familiar it's because they are the true primary colours as used in printing inks.
The addative primaries of light are the subtractive secondaries of pigments/paint, and the subtractive primaries of pigment/paint are the secondary colours of light.
This means that red, white and blue flags such as the Union Jack or the Stars and Stripes do not have any (subtractive) primary colours in them.
So red and blue are not really primary colours in a paint box! But, if you substitute magenta for 'red' and cyan for 'blue' they will be primaries and you will have much more success in mixing paints.
Some artists' paint manufacturers include process cyan, process magenta and process yellow in their ranges. If not quinqcridone magenta, phthalocyanine blue and cadmium yellow are close substitutes for the three primary colours.
A colour wheel is simply a slice of a rainbow, the visible colour spectrum, bent around to form a circle.
Images from http://en.wikipedia.org/wiki/Shades_of_orange
Unfortunately a lot of the colour wheels around still use red blue and yellow as the primaries with violet, green and orange as the secondaries, and then go on to call the in between secondary colours such as yellow-green or blue-violet tertiary colours, which they are not!
Tertiary colours are those hues which are made up from varying proportions of all three secondary colours - the browns, beiges, fawns, khakis and greys.
A colour wheel such as this one is technically more correct.
For paints and pigments cyan, magenta and yellow are the primaries, blue red and green are the secondaries and anything inbetween such as blue-cyan, blue-magenta, red-magenta, orange, green-yellow and green-cyan are are sub-secondaries, ie secondary colours which lean towards on or other of the primaries.
Introducing the third primary to any secondary colour will produce a duller tertiary colour.
This image shows saturated colours in the middle circle with tints in the inner circle and shades in the outer circle, but unfortunately the primary/secondary/tertiary descriptions are incorrect.
Adding white to any colour makes a lighter tint of that colour as shown in the inner circle.