The first draw from a bag with \(2\) red and \(1\) blue determines the winner: A wins red and B wins blue. A later bonus after red does not change the winner. Compute both win probabilities and evaluate fairness.

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A wins with probability 2/3 and B with 1/3; a later bonus after red does not change the winner probabilities, so the game is unfair.

Require red-red for A: P(A)=1/3 and P(B)=2/3, so call the game unfair in B's favor.

Treat the later bonus as changing the winner: P(A)=P(B)=1/2, so call the game fair.

Use first-draw probabilities A=2/3 and B=1/3, but call the game fair because both colors can occur.

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Curriculum context

Course: Math III
Standard: S-MD.6
Category: Statistics and Probability
Domain: Using Probability to Make Decisions
Objective: Use probabilities to make fair decisions in more complex settings.
Problem type: Account for stage-dependent win paths