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The ‘stop after k girls or N children’ policy

Published online by Cambridge University Press:  25 August 2015

Michael de Villiers
Affiliation:
School of Science, Mathematics & Technology Education, University of KwaZulu-Natal, South Africa, e-mail: profmd@mweb.co.za,
Michael Fox
Affiliation:
2 Leam Road, Leamington Spa CV31 3PA e-mail: michaelandjean.fox@btinternet.com

Extract

1. Introduction

In the article [1], a follow-up to my article [2], Christian and Trustrum cite empirical evidence that the probability of a family giving birth to a boy or to a girl may vary from family to family. Letting bi and gi = 1 − bi respectively denote the probability of the ith family giving birth to a boy or to a girl, the suggestion is that bi may be distinct from bj for distinct i and j. As they point out, this has implications for the expected society-wide number of boys and girls. Following my discussion of the ‘stop after k girls’ policy, Christian and Trustrum introduce the related policy ‘stop after k girls or N children’. They argue that the expected number of children under this latter policy is an increasing function of bi (when 0 < k < N). The present article complements their discussion by examining this alternative stopping policy in more detail.

Type
Research Article
Copyright
Copyright © The Mathematical Association 2014

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References

1. Allaire, Patricia R., Zhou, Junmin and Yao, Haishen, Proving a nineteenth century ellipse identity, Math. Gaz. 96 (March 2012) pp. 161165.Google Scholar
2. The Geometer’s Sketchpad, Gregory ellipse quadrilateral generalisation, accessed June 2014 at: http://dynamicmathematicslearning.com/gregory-ellipse.html Google Scholar