### Instruction: 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.### Response: To find the expected value of a random variable, I need to multiply each possible outcome by its probability, and then add up those products.
In this case, the possible outcomes are 0, 2, 4, and 6 dollars, and the probabilities are 1/2, 1/6, 1/6, and 1/6 respectively.
So, the expected value is 0*(1/2) + 2*(1/6) + 4*(1/6) + 6*(1/6) = 0 + 1/3 + 2/3 + 1 = 2 dollars.