Abstract
Initially proposed by Martin Gardner in the 1950s, the famous two-children problem is often presented as a paradox in probability theory. A relatively recent variant of this paradox states that, while in a two-children family for which at least one child is a girl, the probability that the other child is a boy is 2/3, this probability becomes 1/2 if the first name of the girl is disclosed (provided that two sisters may not be given the same first name). We revisit this variant of the problem and show that, if one adopts a natural model for the way first names are given to girls, then the probability that the other child is a boy may take any value in . By exploiting the concept of Schur-concavity, we study how this probability depends on model parameters.
Acknowledgments
The authors would like to thank the Editor, the Associate Editor and two referees for the careful reviews of the manuscript and insightful comments and suggestions. The present work results from exchanges following a talk of the Altaïr conference cycle in Brussels; we would like to thank the organizers.
Disclosure Statement
The authors report there are no competing interests to declare.
Notes
1 In the rest of the article, “name” will throughout stand for “first name”.