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# expected value

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In a game that costs $\$3$to play, a fair die is rolled. If a five or a six is rolled the player receives$\$6$. If any other number is rolled, the player receives nothing. What is the expected value of the game?

Feb 19, 2021

If you roll a 1, 2, 3, or 4, you earn $3. If you roll a 5 or 6, you earn$6. So, we can write the following:
$$E = \frac{4}{6}(\3) + \frac{2}{6}(\6) = \boxed{\4}$$