Question

In a game with a die and a given probability distribution of payoffs, if the expected value is $0, what should be the payoff of the outcome of 6 to make it a fair distribution?

a. -$11
b. -$12
c. $9
d. $10

Answer 1

To make the distribution fair, the payoff of the outcome of 6 should be $18.

Step-by-step explanation:

To calculate the expected value, we multiply each outcome by its probability and sum up the results. Since the expected value of the game is $0, we can set up the equation:

(1/6)(-6) + (1/6)(-6) + (1/6)(-6) + (1/6)(-6) + (1/6)(-6) + (1/6)(x) = 0

Simplifying and solving for x, we get:

x - 18 = 0

x = 18

Therefore, the payoff of the outcome of 6 to make it a fair distribution is $18. As none of the given options match this, the correct answer would be none of the above.