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6 October, 14:44

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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  1. 6 October, 18:40
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    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
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