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?

Question

Mathematics

Nolan Cameron

17 April, 07:40

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?

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Answers (1)

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Nora Rose · Answer 1

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