Both children boys given at least one son
Question
A mother has two children, and you know that at least one of them is a boy. Assuming boys and girls are equally likely and independent, what is the probability that she has two boys?
Short answer
. Of the equally likely cases BB, BG, GB and GG, the information removes only GG, and BB is one of the three that remain.
Adapted from Zhou, A Practical Guide to Quantitative Finance Interviews, sec. 4.3 Conditional Probability and Bayes' Formula, 'Boys and girls A', p.72; question and answer rewritten by SelfMadeQuant.com.
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Open the worked solutionLessons 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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