In the carnival game Under-or-Over-Seven, a pair of fair diceis rolled once, and the resulting sum determines whether the player wins or loses his or her bet. For example, the player can bet $1 that the sum will be under 7that is, 2, 3, 4, 5, or 6. For this bet, the player wins $1 if the result is under 7 and loses $1 if the outcome equals or is greater than 7.

What is the expected value of the player's earning?

Following die-sum frequency table (taken from slides) might help you to calculate the probabilities relevant to the expected value.

Die Sum. /Frequecy

2 1

3 2

4 3

5 4

6 5

7 6

8 5

9 4

10 3

11 2

12 1

Sum 36