Role-playing games like dungeons & dragons use many different types of dice. suppose that a eight-sided die has faces marked 1, 2, 3, 4, 5, 6, 7, 8. the intelligence of a character is determined by rolling this die twice and adding 1 to the sum of the spots. the faces are equally likely and the two rolls are independent. what is the average (mean) intelligence for such characters?

In this question, you are given the number of dice faces (8 faces) and the number of the roll (2 rolls then add 1 value). You are asked the average value.

First, you need to count the average value of the dice probability. Since the lowest possible is 1 and the highest possible is 8, then the dice average value would be: (1+8) / 2 = 4.5

Then, the average intelligence of the character would be : 2 dice + 1 = 2 (4.5) + 1 = 10 intelligence