Compute group probabilities and expected attempts for the reroll method and the double-mapped-A method, then compare fairness and efficiency as separate properties.

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Method 1: fair, 1 attempt. Method 2: fair, 1 attempt. The methods are equally efficient.

Method 1: not fair, 4/3 attempts. Method 2: not fair, 1 attempt. Method 2 needs fewer attempts.

Method 1: fair, 3/4 attempt. Method 2: not fair, 1 attempt. Method 1 needs fewer attempts.

Method 1: fair, 4/3 attempts. Method 2: not fair, 1 attempt. Method 2 needs fewer attempts.

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Curriculum context

Course: Math II
Standard: S-MD.6
Category: Statistics and Probability
Domain: Using Probability to Make Decisions
Objective: Use probability to make fair decisions, such as lotteries or random selection.
Problem type: Compare selection methods by fairness and expected attempts