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Payout mechanism
After you state your guesses about the probability of each grade, the computer will randomly draw one grade to be payoff-relevant.
Subsequently, the computer will randomly draw two numbers, X and Y, each with values between 0 and 100. For each draw, each number is equally likely to be selected. Draws are independent in the sense that the value selected for X in no way affects the value selected for Y and vice versa.
If the randomly drawn grade matches your actual grade in the exam, then you receive the bonus of 10€ if your guess about the probability of the randomly drawn grade is greater than or equal to either X or Y.
If the randomly drawn grade does not match your actual grade in the exam, then you receive the bonus of 10€ if your guess about the probability of the randomly drawn grade is smaller than either X or Y.
This procedure is designed so that you have the best chance of winning the bonus of 10€ when you truthfully state your guesses about the probability of each grade.