Scenario: Your friend and you decide to bet on a baseball game. You offer to pay $200 if you lose the bet, and your friend has to pay $100 if you win the bet. The probability of your winning or losing the bet is $ \frac{1}{2} $ .
-Refer to the scenario above.The average payoff of the bet is ________.

Question

Quizplus · Accepted Answer

To determine the expected value of the bet, we calculate the probabilities and the payoffs:

Probability of winning: 1/2
Payoff if winning: $100

Probability of losing: 1/2
Payoff if losing: -$200

Expected value = (1/2)($100) + (1/2)(-$200) 
Expected value = $50 - $100 
Expected value = ‒$50

Therefore, the average payoff of the bet is ‒$50, making C the correct answer.

Scenario: Your Friend and You Decide to Bet on a Baseball