
Probability Questions
I really don't get this question and my work's due tomorrow any help is really appreciated!
A game consists of rolling a dodeacahedral (12 faced) die and receiving the dollar amount equivalent to the roll. If the cost to play the game is $5 what is the expected payout for each round that is played?
We're on discrete probability chapter, according to the back of my text book the answer should be $5
I hope someone can help me, thanks in advance!!

For discrete random variables, $\displaystyle E(X) = \sum_{i=1}^{n}x_{i}P(X=x_{i})$
Therefore, if $\displaystyle x_{i} = i \mbox{ for }i=1, 2, 3,...,12$
Then, $\displaystyle E(X) = \sum_{i=1}^{12}x_{i}P(X=x_{i})  5$ since you're paying 5 dollars to play.
And $\displaystyle P(X=x_{i}) = \frac{1}{12} \mbox{ for } i = 1, 2, 3,..., 12$ since the die is a fair dodecahedron die.
Thus, $\displaystyle E(X) = [(1)\frac{1}{12} + (2)\frac{1}{12} + (3)\frac{1}{12} + ... + (12)\frac{1}{12}]  5$