Two six-sided dice are rolled. If the sum of the dots showing is odd, we get $17; otherwise, we lose $21. What is the expected value of this game
36 possible outcomes ... 2 through 12
number ... ways
2 ... 1
3 ... 2
4 ... 3
5 ... 4
6 ... 5
7 ... 6
8 ... 5
9 ... 4
10 ... 3
11 ... 2
12 ... 1
equal probability for odd and even ... expected value = .5 * 17 - .5 * 21