The Boy or Girl Paradox

There are many paradoxes or seeming paradoxes in the A Hen and a Half (Ahaah) book.

This is another famous paradox that has mystified people for years! It takes the form of 2 similar but different questions. The second question provides an unusual answer that is the paradox.

Question 1: Mrs Jones has 2 children. The eldest is a girl. What are the chances of the other child being a girl?

Answer 1: 50%

As we would expect, because there are 4 total possible scenarios as follows:

** Oldest Youngest**

G G

** **G B

B G

B B

And two of the possibilities with a Boy as the eldest can’t be, so leaves 2 possible outcomes being either a Girl and a Boy or 2 Girls, making a 50% chance of the second child being a girl.

Question 2: Mr & Mrs Smith have 2 children. One of their children is a boy. What are their chances of the other child also being a boy. Most people would say 50% as there is a 50/50 chance of having a boy or a girl as in Q1. However;

Answer 2: 33%

WHY?

As in Q1, the possible combinations of Male or Female children, in order of birth, are 4-fold:

** Oldest Youngest**

G G

** **G B

B G

B B

We know that one child is B, so GG can be eliminated. That leaves BB, BG or GB

As we already have one Boy – for the second child, that leaves 3 possibilities, being of 1 for a Boy and 2 for a Girl.

So, the chances of Mr and Mrs Smith having 2 boys is 33% not 50%. And that's the paradox that everyone swears by!

Reflect and have a think before you look at my challenge in the Ahaah Paradox Solution!

© Tarquin Group