Question 281388
I would first set up a table where P(x) is the probability for event x and the outcome if x happens (or Y). For example, your question would start like this. Some basic information is that a die has 6 sides, therefore a fair die has a probability of landing 1/6 on each side.

X -- P(x) --  Y
1 -- 1/6  --  -$1
2 -- 1/6  --  -$2
3 -- 1/6  --  +$9
4 -- 1/6  --  +$9
5 -- 1/6  --  -$2
6 -- 1/6  --  -$1

When you have a table like this, you want to multiply each P(x) * y and add them up.

So in your case we would get:

 1/6 * -$1
+1/6 * -$2
+1/6 * +$9
+1/6 * +$9
+1/6 * -$2
+1/6 * -$1

= $(-1/6 - 2/6 + 9/6 + 9/6 - 2/6 - 1/6) (It is helpful if you keep the same denominator)

= + $12/6 = $2

$2 is the expected value. What this represents is that if you somehow played infinite games, you would win an average of $2 per game.