Final answer:
To calculate the expected profit from this game, we multiply each payoff by its probability and sum up the results. The expected profit from this game is $2.25.
Step-by-step explanation:
To calculate the expected profit from this game, we need to find the average value of the payoffs and their corresponding probabilities.
The die has 4 sides, numbered 1-4. The payoffs are $10 for rolling a 1, $5 for rolling a 2 or 3, and -$6 for rolling a 4. Each outcome has a probability of 1/4 since the die is fair.
We calculate the expected profit by multiplying each payoff by its probability, and then summing up the results:
Expected profit = (10 * 1/4) + (5 * 1/4) + (-6 * 1/4) = $2.25
Therefore, the expected profit from this game is $2.25, rounded to the nearest cent.