Expected Value Calculation from Die Rolling Game

Consider a game where you roll a fair six-sided die. If you roll a 1, 2, or 3, you gain that many dollars, and if you roll a 4, 5, or 6, you lose that many dollars. Calculate the expected value of your winnings in this game.

To find the expected value (EV), we need to determine the winnings for each possible roll and their associated probabilities. The winnings for each roll of the die are:

• Roll 1: Gain $1 (Probability = 1/6)
• Roll 2: Gain $2 (Probability = 1/6)
• Roll 3: Gain $3 (Probability = 1/6)
• Roll 4: Lose $4 (Probability = 1/6)
• Roll 5: Lose $5 (Probability = 1/6)
• Roll 6: Lose $6 (Probability = 1/6)

Calculate the expected value using the formula:

$$ EV = ext{Sum of (Value * Probability)} $$