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?

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 = 0.5

Since 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  0.25

A              3       -2     -2       1

E(A)      0.75   -0.5    -0.5   0.25   =    0

The game is a fair game with equal expected values for A and B.

It does not matter whether to be A or B