Problem

For A, B, and C, M1 gives probabilities \(1/3\) each with expected draws \(1\); M2 gives \(1/3\) each with expected draws \(10/9\); M3 gives \(0.4\), \(0.3\), \(0.3\). Apply exact fairness first, then smallest expected draws, and recommend a method.

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What this problem is really about

When criteria are ordered, treat the first one as a gate rather than blending everything into one score. Remove any method that fails exact fairness, even if it looks efficient. Only then compare the eligible methods on the second criterion, using the same expected-draw unit, so the recommendation follows the rule in the order given.

Answer choices

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M1 and M2 are fair while M3 has .4,.3,.3; choose M3 by incorrectly treating those probabilities as equal.

M1 is fair with expected 1 draw, M2 fair with 10/9, and M3 unfair; choose M2 by incorrectly requiring a reroll.

M1 and M2 are fair while M3 has .4,.3,.3; choose M3 because it accepts every draw, violating the fairness-first rule.

M1: the 12-sector spinner gives 1/3 each with expected draws 1; M2 is fair but needs 10/9 draws; M3 is unfair. Choose M1.

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For A, B, and C, M1 gives probabilities \(1/3\) each with expected draws \(1\); M2 gives \(1/3\) each with expected draws \(10/9\); M3 gives \(0.4\), \(0.3\), \(0.3\). Apply exact fairness first, then smallest expected draws, and recommend a method.

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