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?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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,...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

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 

Approved by eNotes Editorial Team