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There are two different colour systems, additive and subtractive.

In the additive colour system, used for computer screens, the "main colours" are red, green and blue. It starts with a black screen and adds light to the black

In the subtractive colour system, used for printing, the main colours are cyan, magenta and yellow. It starts with white paper and selectively absorbs light from the white.

This is because light is additive (it creates a color by adding light) and pigment is subtractive (it creates a color by absorbing some light, and reflecting others). Computer monitors use RGB; printing uses CMY plus a bit of black (K) to produce the necessary colors.

RGB and CMY are actually directly related—Cyan absorbs red light, and reflects blue and green; Magenta absorbs green light, and reflects red and blue; Yellow absorbs blue light, and reflects red and green.

RGB are primary colours. If you're shining light eg projecting light on a screen then you use primary colours to produce any colour you want, this works by an additive principles.

CMY are secondary colours. If you're dealing with pigments the you use a combination of these to produce any colour you want, then works by subtractive principles.