Why rgb and not cmy?
There's a difference between additive colors (http://en.wikipedia.org/wiki/Additive_color) and subtractive colors (http://en.wikipedia.org/wiki/Subtractive_color).
With additive colors, the more you add, the brighter the colors become. This is because they are emitting light. This is why the day light is (more or less) white, since the Sun is emitting in almost all the visible wavelength spectrum.
On the other hand, with subtractive colors the more colors you mix, the darker the resulting color. This is because they are reflecting light. This is also why the black colors get hotter quickly, because it absorbs (almost) all light energy and reflects (almost) none.
Specifically to your question, it depends what medium you are working on. Traditionally, additive colors (RGB) are used because the canon for computer graphics was the computer monitor, and since it's emitting light, it makes sense to use the same structure for the graphic card (the colors are shown without conversions). However, if you are used to graphic arts and press, subtractive color model is used (CMYK). In programs such as Photoshop, you can choose to work in CMYK space although it doesn't matter what color model you use: the primary colors of one group are the secondary colors of the second one and viceversa.
P.D.: my father worked at graphic arts, this is why i know this... :-P
The difference lies in whether mixing colours results in LIGHTER or DARKER colours. When mixing light, the result is a lighter colour, so mixing red light and blue light becomes a lighter pink. When mixing paint (or ink), red and blue become a darker purple. Mixing paint results in DARKER colours, whereas mixing light results in LIGHTER colours. Therefore for paint the primary colours are Red Yellow Blue (or Cyan Magenta Yellow) as you stated. Yet for light the primary colours are Red Green Blue. It is (virtually) impossible to mix Red Green Blue paint into Yellow paint, or mixing Red Yellow Blue light into Green light.
the 3 additive colors are in fact red, green, and blue. printers use cmyk (cyan, magenta, yellow, and black).
and as http://en.wikipedia.org/wiki/Additive_color explains: if you use RYB as your primary colors, how do you make green? since yellow is made from equal amounts of red and green.
The basic colours are RGB not RYB. Yes most of the softwares use the traditional RGB which can be used to mix together to form any other color i.e. RGB are the fundamental colours (as defined in Physics & Chemistry texts).
The printer user CMYK (cyan, magenta, yellow, and black) coloring as said by @jcomeau_ictx. You can view the following article to know about RGB vs CMYK: RGB Vs CMYK
A bit more information from the extract about them:
Red, Green, and Blue are "additive colors". If we combine red, green and blue light you will get white light. This is the principal behind the T.V. set in your living room and the monitor you are staring at now. Additive color, or RGB mode, is optimized for display on computer monitors and peripherals, most notably scanning devices.
Cyan, Magenta and Yellow are "subtractive colors". If we print cyan, magenta and yellow inks on white paper, they absorb the light shining on the page. Since our eyes receive no reflected light from the paper, we perceive black... in a perfect world! The printing world operates in subtractive color, or CMYK mode.