{{ block title }} Different Beliefs for each Box {{ endblock }} {{ block content }}
Every round, you and another participant (participant 2) bet on the probability the computer selected the Yellow box to generate the observed sequence. You and participant 2 will observe the same sequence of ten marbles drawn randomly from either a Yellow or Green box.
You know that the computer selects the Yellow box with 90% probability and the Green box with 10% probability. However, you will be matched with the answers from participant 2 who beliefs that the computer selects the Yellow box with 20% probability and the Green box with 80% probability. These probabilities will be the same every round.
In each round, you and participant 2 make a bet with the probability that the sequence observed came from a Yellow box. Also, you must estimate participant 2’s bet for the Yellow box.
Notice that you and participant 2 have a different belief about the probability that the computer selects the Yellow box. However, both observe the same sequence. The next table summarizes the associated probabilities to each participant:
| Box | Probability that the computer selects each box | Participant 2's believed probability that the computer selects each box |
|---|---|---|
| 90 | 20 | |
| 10 | 80 |