This a not a easy question indeed. There are many tiny particles in the sky. They can scatter the optical wave and the optical wave at the short wavelength, such as blue light, are easier to be scattered. The scattered light propagate towards all directions around. This makes the sky looks blue.
Air scatters more blue light downwards than other colours, so when we look up, it seems blue. There is not much around to scatter the sunlight (or starlight) when we are in space, so it looks black.
If you are high up in an aeroplane, the sky (upwards) looks dark blue.
It’s because of a phenomenon called Rayleigh scattering. As both Tom and Tianfu say, blue coloured light is scattered more easily than red so more blue light is scattered sideways from the atmosphere toward the earth than the other colours.
Incidentally, this is the same reason that sunsets and sunrise appear red. The whitish light from the sun passes through the atmosphere towards us, and lots of the blue is removed by the Rayleigh scattering leaving the reds and yellows behind to make a sunset. It helps that the sun’s light has to pass through a greater distance of atmosphere when it’s setting (because it’s at a shallow angle to our part of the world) so the scattering effect is enhanced.
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