A random draw selects which question will be paid at the end of the experiment.
If Questions 1 or 2 are selected by the random draw, you will be paid the bonus if your answer is correct.
If Question 3 is the one selected, the probability you select as an answer will define whether your payment depends
on the statement in Question 3 being true, or on a random lottery.
- The computer will generate a lottery box with 100 balls, with a random proportion of purple balls (from 1 to 100).
Note: all proportions of purple balls are equally likely (have the same probability of happening).
- Your reported probability defines if your bonus will depend on the statement in Question 3 being indeed true, or on a random draw from the lottery box. How?
- If the box has a higher number of purple balls than your reported probability:
A ball will be randomly drawn from the box. If it is purple, you win.
- If the box has a lower or equal number of purple balls than your reported probability:
The statement in Question 3 is checked. If it was indeed true, you win.
- Your bonus depends on the lottery only when the probability of wining it is higher than your reported probability of Question 3 being true.
Therefore, the method applied will always favour your probability to earn the bonus.
>Example:
- Imagine you reported a probability of 20 percent that the statement in Question 3 is true.
- The computer randomly generated a box with 100 balls, 40 of which are purple.
- This means the probability to randomly draw a purple ball from the box is 40 percent.
Since 40 (purple balls) is higher than 20 (reported probability):
- Your payment depends on the box, and it does no longer matter whether the statement in Q3 is true or false.
- A ball will be randomly drawn from that box: if it is purple, you win the bonus. Otherwise, you don't.
- Imagine instead that you had reported a probability of 60 percent that the statement in Question 3 is true.
- This time, the computer randomly generated a box with 100 balls, 50 of which are purple.
Since 60 (reported probability) is higher than 50 (purple balls):
- Your payment depends on the statement in Question 3, and the lottery box no longer matters in this case.
- The statement in Question 3 is checked: if it is true, you win the bonus. Otherwise, you don't.