{{ 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

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