Consider a variant of the information cascades problem we look at in lecture:

• A jar is sitting on the instructor's desk in the front of the room. Students cannot see what is inside the jar.

With probability 1/2 the jar containssixred marbles andfourblue marbles and with probability 1/2 it containsfourred marbles andsixblue marbles.

If the jar contains six red marbles we will call it R; if it contains six blue marbles we will call it B.

One by one students will come to the front of the room, pull a marble out of the jar, and then announce to the class whether they believe the jar is R or it is B. They then return the marble to the jar without showing it to the class.

After everyone has made their guess the instructor tells the class whether the jar was R or B. Students who guessed correctly get a payoff of 1; students who guessed incorrectly get a payoff of 0.

We said that if the first student guessed R and the second student saw a red marble the second student would also guess R, but that if the first student guessed R and the second student saw a blue marble the second student would guess B.

Use Bayes' rule to answer the following question: if the first two students guess that the jar is R, will the third student guess that the jar is R if the third student sees a blue marble? Defend your answer carefully.