# The Birthday “Problem” in Python

A few days ago I found myself having a vague recollection of an interesting statistics problem. All I could remember was that it had to do with having a room full of people and the probability that any two people in that room would have the same birthday. I remembered the point, which was that it is much more likely than you might think, but I was fuzzy on the details.

After trying to define the problem and find an answer mathematically, I remembered that I suck at statistical reasoning about as much as the average person. So I decided to model the problem with a short Python script and find the answer that way.

Sure, I could’ve looked it up, but where’s the fun in that?

The problem: There are n people (say, at a party) drawn randomly from a population in which the chances of having a birthday on any day is equal to having a birthday on any other (which is not true of real populations (probably)). What is the probability of there being at least two people with the same birthday in the sample?

To put this thing together, I figure we need three things:

1. The ability to generate random numbers (provided by Python’s random module);
2. An object representing each person;
3. A party object full of those people.

Then we can add things like the ability to choose how many people we want at the party and how many parties to have, as well as some output for making plots!

First, the Person object. All each person needs is a birthday:

```import random
random.seed()

class Person:
def __init__( self ):
self.birthday = random.randint( 1, 365 )
```

# More Puzzling

In a previous post, I discussed my attempt to write a program to solve a puzzle. I never updated that post because, well, I ran the program all night and it didn’t find the solution!

I had made up a fake puzzle that I knew had a solution for testing, and the program could solve it in 15 minutes. But it couldn’t solve the one I had recorded for the real puzzle. I figured (and hoped) that I had simply recorded it wrong and to check, I re-recorded the pieces and tried again. And it worked! Here’s how:

# A simple model of selection

Inspired by Dawkins’ METHINKS IT IS LIKE A WEASEL program (hereafter just weasel) described in his book “The Blind Watchmaker,” and wanting to practice my blossoming C++ skills, I decided to write my own version of weasel. It was successful enough, and I found the results interesting enough to warrant discussion. Download the program (Windows .exe file) so you can try it out for yourself (and you can also get the source code if you want). In this post I’ll discuss what the program does and why. In the next post I’ll talk a bit about the results of the program.