A little nitpicking about the "2 dice" thing : usually when you throw you two dices, it doesn't matter which dice gives which result. Sure you could use colored dices and have the "blue 2, red 3" be different than "blue 3, red 2", but that's very rarely the case. Usually you do the sum (or look for patterns like doubles) but "2, 3" and "3, 2" are equivalent, and in that case the entropy isn't the double, but lower.

What you wrote is technically right - but goes against the common usage of dices, so it would be worth adding a footnote or precision about that, IMHO.