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Two girls – the value of information

Published online by Cambridge University Press:  23 January 2015

Keith Parramore  and
Joan Stephens
Keith Parramore
Affiliation:
1 Falmer Avenue, Goring-by-Sea, Worthing BN12 4SY, e-mail: parramore@ntlworld.com
Joan Stephens
Affiliation:
e-mail: joan.stephens@ntlworld.com
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Extract

We came across the ‘two girls’ version of the children's gender problem nearly 35 years ago. How we came to it we cannot remember, but Martin Gardner had published a variant of it in the Scientific American in 1959. It re-emerged for us in the summer of 2010, following the publication of an article in Science News [1]. Subsequently Keith Devlin wrote about how this re-emergence impacted on him, and noting that ‘Probability Can Bite“ [2]. The mathematics herein reflects and extends that in Devlin's article.

In case the reader has not encountered the problem before, we first pose four problems.

1. A family has two children. One of them is a girl. What is the probability that they are both girls?

2. A family has two children. The younger is a girl. What is the probability that they are both girls?

3. A family has two children. One of them is a girl, and she was born on a Tuesday. What is the probability that they are both girls?

4. A family has two children. One of them is a girl, and she has green hair. What is the probability that they are both girls?

Type
Articles
Information
The Mathematical Gazette , Volume 98 , Issue 542 , July 2014 , pp. 243 - 249
Copyright
Copyright © Mathematical Association 2014 

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References

1. Rehmeyer, J., When intuition and math probably look wrong, Science News (June 28th 2010), available at www.sciencenews.orglarticle/when-intuition-and-math-probably-look-wrong Google Scholar
2. Devlin, K., Probability Can Bite, Mathematical Association of America (2010, April) available at www.maa.orglexternal_archive/devlinldevlin_04_1O.htm Google Scholar
3. Grinstead, and Snell, , Introduction to Probability, The Chance Project (4 July 2006), available at http://math.dartmouth.edu/~prob/prob/prob.pdf Google Scholar
4. D'Agostini, G., On the so called Boy or Girl Paradox, Cornell University Library, arXiv:1001.0708v1 [Math.HO] (January 2010), available at http://arxiv.orgiabs/l001.0708v1 Google Scholar
5. Wikiepedia (n.d.). Boy or Girl Paradox, accessed on August 22, 2013 at http://en.wikipedia.org/wiki/Boy_or_Girl_paradox Google Scholar