Sunlight contains visible and invisible parts or electromagnetic spectrum.
The visible colors of light are violet, indigo, blue, green, yellow, orange, red (VIBGYOR).
According to the Rayleigh's criterion, the intensity of scattered light is inversely proportional to the fourth power of the wavelength if the size of the scatterers are of the order of the wavelength of light. Air molecules have their size of this order. Thus shorter wavelength of blue (450 nm) is scattered much more than the longer wavelength of red (700nm).
Thus the sky looks blue
Violet color has even shorter wavelength (330nm) but the sky does not look violet. There are two reasons for this.
a) The percentage of violet color is lesser in sunlight than blue color.
b) There are three types of cone cells in our eyes which are sensitive to colors; blue, red and green
The blue cone cells are sensitive to colors around the blue, such as, violet and green. However they are most sensitive to blue and their sensitivity to violet drops greatly.