Q:

Two players A and B play a marble game. Each player has both a red and blue marble. They present one marble to each other. If both present red, A wins $3. If both present blue, A wins $1. If the colors of the two marbles do not match, B wins $2. Is it better to be A, or B, or does it matter?

Accepted Solution

A:
Answer:Step-by-step explanation:A has one red and blue marble and B has one red and blue marble.Hence selecting one marble is equally likely with prob = 0.5Since A and B are independent the joint event would be product of probabilities.Let A be the amount A wins.If each selects one, the sample space would be              (R,R)  (R,B)  (B,R) (B,B)Prob     0.25  0.25  0.25  0.25A              3       -2     -2       1E(A)      0.75   -0.5    -0.5   0.25   =    0The game is a fair game with equal expected values for A and B.It does not matter whether to be A or B