Final answer:
The player should win $55 when they win in order for the game to be fair.
Step-by-step explanation:
Theory:
In order for the game to be fair, the expected value of the game should be $0.
Calculation:
Let's calculate the expected value of the game:
Probability of rolling a 3 (winning): 1/6
Expected win: Probability of winning * Amount won = (1/6) * X
Probability of not rolling a 3 (losing): 5/6
Expected loss: Probability of losing * Amount lost = (5/6) * (-11)
Setting the expected value to $0 and solving for X:
(1/6) * X + (5/6) * (-11) = 0
X/6 - 55/6 = 0
X/6 = 55/6
X = 55
Answer:
In order for the game to be fair, the player should win $55 when they win.