What is the expected value of a single fair die roll?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

What is the expected value of a single fair die roll?

Explanation:
Think of the expected value as the average outcome you’d get if you rolled the die many times. Each face 1 through 6 is equally likely, so you average all possible results: (1 + 2 + 3 + 4 + 5 + 6) / 6 = 21 / 6 = 3.5. Because the distribution is symmetric, the mean sits at 3.5. Remember, you can’t roll a 3.5 on a single turn—the expected value is the long-run average over many rolls.

Think of the expected value as the average outcome you’d get if you rolled the die many times. Each face 1 through 6 is equally likely, so you average all possible results: (1 + 2 + 3 + 4 + 5 + 6) / 6 = 21 / 6 = 3.5. Because the distribution is symmetric, the mean sits at 3.5. Remember, you can’t roll a 3.5 on a single turn—the expected value is the long-run average over many rolls.

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