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?
+1223 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:
\(E = \frac{4}{6}(\$3) + \frac{2}{6}(\$6) = \boxed{\$4}\)
