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 bo

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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 bo

th 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?

Mathematics

1 answer:

Zina [12.3K] · Answer 1 · 2026-02-21T16:20:00+03:00

Answer:

Step-by-step explanation:

Player A has a red marble and a blue marble, while Player B also has a red marble and a blue marble.

Therefore, the probability of selecting one marble is equal, at 0.5.

Due to the independence of A and B's choices, the joint event is calculated by multiplying the probabilities.

Let A represent the amount that player A wins.

If both players select one marble, the sample space can be considered as

(R,R) (R,B) (B,R) (B,B)

Probability 0.25 0.25 0.25 0.25

A's winnings 3 -2 -2 1

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

Thus, the game is even, offering equal expected values for both A and B.

It does not influence the outcome whether you are A or B.

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 bo

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Derivation of Formulas