For a fair \(A/B\) result, M1 uses one fair-coin flip and has expected device uses \(1\); M2 is fair conditionally but has expected flips \(6.25\). Apply the expected-use limit of \(1.2\) and recommend an eligible method.

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M1 meets the 1.2 limit; M2 exceeds it with expected 6.25, but choose M2 because accepted-pair probability is .32.

M1 is fair with expected use 1; M2 is fair with expected 6.25, but choose M2 because its accepted pairs are balanced.

Choose M1, one fair-coin flip: expected uses 1. M2 is fair but needs 6.25 flips on average.

M1 is a fair method with expected use 1, but choose neither by incorrectly claiming no fair-coin method exists.

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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: Choose among fair methods using stated criteria