This question is from Game Theory

Consider the following process: An instructor has two cups behind a screen. Cup A has 8 marbles and Cup B has 10 marbles. In cup A, there are 5

blue marbles and 3 red marbles. In cup B, there are 4 blue marbles and 6 red marbles. The instructor randomly picks one of the two cups to draw marbles from. Which cup the instructor has chosen is not revealed.

(a) What is the likelihood a marble is drawn from cup A? cup B?

(b) Suppose the instructor draws and reveals a blue marble. Use

Bayes Rule to update your beliefs that the instructor is drawing

marbles from cup A. From cup B.

(c) The instructor replaces the blue marble in its original cup and

draws another marble. The second marble drawn is blue. Using

Bayes Rule to update your beliefs that the instructor is drawing

marbles from cup A. From cup B.

(d) Write a brief essay on when/why Bayes Rule is important in

games of incomplete information