Expected Value and Variance of a Dice Game

Consider a game where a participant can make a series of bets on a fair six-sided die. The participant receives a payout based on the outcome of the die roll as follows:

• If the die shows 1 or 2, the participant loses $10.
• If the die shows 3 or 4, the participant wins $5.
• If the die shows 5 or 6, the participant wins $20.

Calculate the expected value (EV) of this game and the variance of the payout. Remember that the expected value is calculated as follows:

$$EV = ext{Probability} imes ext{Payout}$$

Finally, evaluate which option correctly identifies the expected payout rounded to two decimal places and the variance of the payout.