Mother of two at a conference for parents of girls

Question

Only parents who have at least one daughter may attend a certain conference. Jane, who has two children, receives an invitation. Assuming each child is independently a boy or a girl with equal probability, what is the probability that both of Jane's children are girls?

Short answer

$\tfrac13$ . The invitation only tells us that Jane's family is not boy–boy. Of the three remaining equally likely ordered families (girl–boy, boy–girl, girl–girl), just one has two daughters.

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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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