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jmc

counting and probability junior

Problem

A fair 6-sided die is rolled. If the roll is even, then you win that amount of dollars (so that, for example, if you roll 4, then you win \4$). If the roll is odd, you win nothing. What is the expected value of your winnings? Express your answer as a dollar value.
Solution
There is a probability of rolling an odd number and winning \0\dfrac{1}{6}\, \4\. So E = \dfrac{1}{2}\times \0 + \dfrac{1}{6}\times(\2+\4+\6) = \boxed{\2}$.
Final answer
\$2