* * * * *
                                        
                          1/2 of a 2/3 spherical cow …
                                        
> Today's post is a simple question.
> 
> Let's say, hypothetically speaking, you met someone who told you they had
> two children, and one of them is a girl. **What are the odds that person
> has a boy and a girl?**
> 
> Consider your answer carefully, without doing a web search, or reading the
> comments to this post. Don't cheat—but be prepared to explain your
> reasoning, because the solution might surprise you.
> 
> It's almost like some kind of conspiracy [1] or something.
> 

“Coding Horror: The Problem of the Unfinished Game [2]”

Obigatory Sidebar Links

* The Problem of the Unfinished Game [3]
* Finishing The Game [4]
* Reddit Thread on “Finishing The Game” [5]
* Hacker News Thread on “The Problem of the Unfinished Game” [6]
* Hacker News Thread on “Finishing The Game” [7]


That, and the follow-up post [8], plus a few threads on various commentary
sites can be summed up with the following result:

> The odds are 1/2, except, of course, when it's 2/3.
> 

A lot of virtual ink has been spilled over this, but I think I have this down
now. I wrote a program to simulate this problem and doing so has clarified
the result (nothing like picking a few million pairs of virtual kids and
seeing actual numbers).

It goes like this. Assume a spherical cow [9] … oh wait, wrong problem.
Assume an even 50% chance of having a boy or a girl. Take 100 families with
two kids. There are four cases to contend with, boy/boy (25%, or 25 out of a
100 families), boy/girl (25%, or again, 25 out of 100 families), girl/boy
(25%) and girl/girl (the remaining 25%). But in three of the four cases (75%)
there is at least one girl. And out of those 75 families, 50 of them (or 66%
of 75, or 2/3) will have a boy.

And thus, that's how we end up with 1/2 of a 2/3 spherical cow.

[1] http://www.codinghorror.com/blog/archives/000850.html
[2] http://www.codinghorror.com/blog/archives/001203.html
[3] http://www.codinghorror.com/blog/archives/001203.html
[4] http://www.codinghorror.com/blog/archives/001204.html
[5] http://www.reddit.com/r/programming/comments/7msca/coding_horror_fini
[6] http://news.ycombinator.com/item?id=415416
[7] http://news.ycombinator.com/item?id=416402
[8] http://www.codinghorror.com/blog/archives/001204.html
[9] http://en.wikipedia.org/wiki/Spherical_cow

Email Sean Conner at sean@conman.org

.