Rolling 2 dice there are 36 possible outcomes.
Sum of 10: 4, 6; 5, 5; 6, 4
3 outcomes have a sum of 10.
Sum of 3: 1, 2; 2, 1
2 outcomes have a sum of 3.
Each play costs $5.
If he rolls a sum of 10, he wins $10, but he paid $5 to play, so for each roll of a sum of 10 he earns $5.
If he rolls a sum of 3, he wins $20, but he paid $5 to play, so for each roll of a sum of 3 he earns $15.
For all the other 31 possible sums, he loses $5.
Add: 3 * $5 + 2 * $15 - 31 * $5 = $110
Now divide the sum by the total number of outcomes.
$110/36 = -$3.05555...
Answer: -$3.06
