Kevin thinks he can use ESP to predict the outcome of rolling a fair die. You agree to pay him $3 if he can correctly predict the results of the next roll. Kevin has to pay you $1 if he is wrong. If Kevin doesn't have any psychic powers, which of the following is closest to the expected value of your net winnings on this bet?
A) -$0.67
B) -$0.33
C) $0
D) $0.33
E) $0.67

Question

Quizplus · Accepted Answer

The expected value of your net winnings can be calculated by considering the probability of each outcome and the corresponding payoff. Since the die is fair, Kevin has a 1/6 chance of predicting the roll correctly and a 5/6 chance of being wrong. If he's right, you pay him $3, and if he's wrong, he pays you $1. The expected value (EV) is calculated as follows: EV = (1/6)*(-$3) + (5/6)*($1) = -$0.50 + $0.83 = $0.33.

Kevin Thinks He Can Use ESP to Predict the Outcome