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# Expected value

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In a game that costs 3 dollars to play, a fair die is rolled. If a five or a six is rolled the player receives 6 dollars. If any other number is rolled, the player receives 1 dollar. What is the expected value of the game?

Aug 14, 2021

Expected value = $$\frac{2}{6}\times 6+\frac{4}{6}\times 1-3=-\frac{1}{3}$$