Dice game A person pays 2 to play a certain game by rolling

Dice game: A person pays $2 to play a certain game by rolling a single die once. If a 1 or a 2 comes up, the person wins nothing. If, however, the player rolls a 3, 4, 5, or 6, the person wins the difference between the number rolled and $2. Find the expected value for this game, i.e., the mean.

Please include all the steps with the answer

Solution

I assume the player wins if the die shows 3,4,5 and 6

Assuming a fair die, all outcomes are equally possible.
The payouts are: 0, 0, 1, 2, 3, 4. Summed and multiplied by 1/6 gives 10/6 = $1.6666...
Subtract the $2 to play the game and the expectation is -$0.33333...
With a negative expectation, the game is not fair.