Final answer:
The expected value of the game is -$1/6, which means that, on average, you would expect to lose $1/6 per game.
Step-by-step explanation:
To find the expected value of the game, we need to calculate the probability and value of each outcome and then sum them up.
There are three possible outcomes when rolling a dice: 2, 4, or 6 with a value equal to the die; and 1, 3, or 5 with a value of -$5.
The probabilities of rolling each number are 1/6, and the values for each outcome are 2, 4, 6, -5, -5, -5. We multiply each value by its respective probability and sum them up to get the expected value: (1/6 * 2) + (1/6 * 4) + (1/6 * 6) + (1/6 * -5) + (1/6 * -5) + (1/6 * -5) = 1/3 - 5/6 = -1/6.
The expected value of the game is -$1/6, which means that, on average, you would expect to lose $1/6 per game.