Exactly one head given at least one in three tosses

Question

Three fair coins are tossed. Someone tells you that at least one landed heads. Given this, what is the chance that exactly one coin landed heads?

Short answer

$\tfrac37$ . Removing $TTT$ leaves 7 equally likely outcomes, and exactly 3 of them ( $HTT$ , $THT$ , $TTH$ ) have a single head.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Conditional Probability, Total Probability, and Bayes' Rule
Worked Examples — Probability Trees, Monty Hall, and Bayesian Updating
Sample Spaces, Events, and the Probability Axioms

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