Use probability to make fair decisions, such as lotteries or random selection.
Decide whether a multi-stage random selection process is fair by comparing each participant's overall probability
Problem
Is this multi-stage selection process fair? A coin chooses the group first, then \(\text{one}\) person is chosen uniformly from groups of sizes \(4\) and \(8\).
Equal probabilities at the group stage do not automatically mean equal probabilities for individuals. We’ll trace one named person through each group branch, multiply the group chance by the within-group chance, compare the terminal per-person probabilities, and judge fairness at the person level.
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