Picking one of three kids fairly with a coin

Question

You have only a fair coin and need to select one of three children so that each child has exactly a one-in-three chance of being chosen. How can you do it?

Short answer

Toss twice and reject one outcome. Assign HH, HT and TH to the three children; if you get TT, discard the pair and toss twice again. The three accepted outcomes are equally likely and the process stops with probability $1$ , so each child is picked with probability $\tfrac13$ .

Adapted from Crack, Heard on the Street, Q4.8, p.38; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Sample Spaces, Events, and the Probability Axioms
Counting and Combinatorics
Conditional Probability, Total Probability, and Bayes' Rule

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