# A post that starts with a brain teaser, moves to a visual, and ends with a stern reminder

I wanted to put up a brain teaser yesterday, but the little one got his first cold.  Baby coughs are sad.

Anyway, one of the more famous statistical brain teasers is the birthday problem.  There are a few variations, but essentially the question goes something like this:

You’re at a party with 23 guests, including you.  What are the chances that  two people there have the same birthday?

The trick of course is that no one has to have a specific birth date, so the answer is not 23/366, but instead around 50% (interestingly, if the party were 50 people, it goes up to 97%).    For a further explanation, see here.

What’s interesting about this problem is that you have to assume every birth date is equally likely…which of course isn’t true.  I’ve written before about uneven distribution of birthdays in the US, due in part to scheduled c-sections or induced labor.  Anyway, I saw an interesting heat map today of birthday distributions from the Daily Viz, which is what got me thinking about the brain teaser.

To note, this chart was made from a list of ranked birthdates, which is here.

I was a little struck by this, because I was thinking about how terrible I am at estimating things like this on my own.  The most common birthday in my circle of friends/family is Halloween.  The first week in April has the birth dates of my mother, sister and husband.  Neither of those time frames are overly popular within the general population, although I’d guess the difference between “most popular” and “least popular” are relatively small.  It was a good reminder that those I spend the most time with are not terribly representative of the population in general, on average.

## 6 thoughts on “A post that starts with a brain teaser, moves to a visual, and ends with a stern reminder”

1. I gather people are looking for things to do indoors in winter.

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2. Folks find that 50% likely at 23 different people so counterintuitive that I have long sought a way to make it seem more plausible. The closest I have come is to move to 183 birthdays – every other one – and ask people how many darts in a row they think they can throw that will fall exactly between dates, never hitting a dart already present. They start to get it. Then you can move to 50 birthdays, and folks can sorta get that throwing a dart and missing ALL of them is going to start being unusual.

It doesn't get you to 23, which still seems counterintuitive no matter how many times you do the math, but it at least gets them closer.

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3. Your grandfather was the one who introduced me to this when I was probably in middle school. Since everything in my life was baseball, I looked at the 40 man rosters for each baseball team and, what did I find? The majority of rosters had two people who shared a birth date. That made me a believer. Sorry about Finn's cold!

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4. There was some entertaining discussion in the comments thread on the original post for that graphic about how this would look if the data were pulled from somewhere in the southern hemisphere. I didn't see any hard data links, but apparently it's reversed.

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5. I like this explanation. You're right, it's a stretch to 23, but it definitely gets people in the right ball park.

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6. Another good example.

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