Revisiting the Name Variant of the Two-Children Problem

Davy Paindaveine and Philippe Spindel

The American Statistician, 2023, vol. 77, issue 4, 401-405

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 (0,2/3) . By exploiting the concept of Schur-concavity, we study how this probability depends on model parameters.

Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/00031305.2023.2173293 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:amstat:v:77:y:2023:i:4:p:401-405

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UTAS20

DOI: 10.1080/00031305.2023.2173293

Access Statistics for this article

The American Statistician is currently edited by Eric Sampson

More articles in The American Statistician from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().