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.
There is a $\dfrac{1}{2}$ probability of rolling an odd number and winning $\$0$, and a $\dfrac{1}{6}$ probability of winning each of $\$2$, $\$4$, or $\$6$.  So $E = \dfrac{1}{2}\times \$0 + \dfrac{1}{6}\times(\$2+\$4+\$6) = \boxed{\$2}$.