Use probabilities to make fair decisions in more complex settings.
Repair an unfair random method with exact probabilities
Problem
A \(10\text{-}\text{sector}\) spinner has three sectors each for A, B, and C plus one extra sector. Give a fair reroll repair and compute conditional probabilities, acceptance per spin, and expected spins.
Big Picture
What this problem is really about
A reroll repair separates a single spin from the eventual completed trial. First make the accepted probability mass equal across participants, then condition on the event that a participant was actually named. Efficiency is a different calculation: find the acceptance chance per spin, and use its reciprocal for the expected number of independent attempts.
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