The Game of Dungeons and Dragons Uses Nonstandard Dice

Short Answer

The game of Dungeons and Dragons uses nonstandard dice. Consider a die with eight sides marked 1, 2, 3, 4, 5, 6, 7, and 8. (In this problem, "an eight" refers to rolling an eight on either or both dice, while "a total of eight" refers to the sum on the two dice.) What is the probability of rolling exactly one two with two such dice?
Give your answer as a fraction.