A fair six-sided die is rolled. What is the expected value of the result?

• A. 3.5
• B. 3
• C. 4
• D. 3.2

Answer: (A)

Expected value is the long-run average outcome you would expect if you rolled the die many times. For a fair six-sided die, each face from 1 to 6 is equally likely, so you take the mean of those numbers: (1 + 2 + 3 + 4 + 5 + 6) / 6 = 21 / 6 = 3.5. This number represents the average result you would approach over many rolls, even though a single roll can’t actually show 3.5. The other options aren’t the average: 3 and 4 are possible individual outcomes, and 3.2 would indicate a different weighting of outcomes, which isn’t the case here.