Why is the daytime sky blue on Earth, black on the Moon, and a reddish tint on Mars?

On Earth, the sky is blue due to the fact that the scattering of sunlight by air molecules is selective: the blue part of the spectrum is scattered more than the red. There is no atmosphere on the moon and therefore there is almost no light scattering. On Mars, due to frequent dust storms, the atmosphere is saturated with the smallest dust particles, which, like the soil, have a red color.