# Role-playing games like Dungeons & Dragons use many different types of dice. Suppose that a four-sided die has faces marked 1, 2, 3, 4. The intelligence of a character is determined by rolling...

Role-playing games like Dungeons & Dragons use many different types of dice. Suppose that a four-sided die has faces marked 1, 2, 3, 4. 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?

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When a four sided die is rolled the probability of each of the outcomes 1, 2, 3 and 4 is 0.25. If two of the dice are rolled the sum can be any of the values in the set {2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 8}

Adding 1 to the final outcome makes the set of values {3, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 8, 6, 7, 8, 9}

The mean outcome is: `(3+ 4+ 5+ 6+ 4+ 5+ 6+ 7+ 5+ 6+ 7+ 8+ 6+ 7+ 8+ 9)/16 = 6`

**The mean intelligence of the characters in the role-playing game is 6**