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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
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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:

\(E = \frac{4}{6}(\$3) + \frac{2}{6}(\$6) = \boxed{\$4}\)

 Feb 19, 2021

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