Curious Paradoxes
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!