Daughter's Questions: Why is the sky blue (or red)?

A few months ago my daughter asked another of her perceptive questions. After asking why the sky is blue, and recieving an explanation, she quickly followed up with a questions about why sunrises and sunsets are red.

I'd been ready with an answer for the first, but not the second and then it quickly turned out that my answer to the first wasn't sufficiently thorough. The answers related to the wavelengths of red and blue light being at opposite ends of the visible spectrum, and the way that light of shorter wavelengths gets more easily diffused as it travels through the atmosphere.

However, blue isn't at the end of the spectrum, violet is. So that should be diffused more in the sky. The sky shouldn't be blue during the day ... it should be violet. Why isn't it?