The geek portion of my brain was catching up from some blog entries over the weekend and on Friday when I was out sick. In doing so, I came across an entry at Coding Horror which, in addition to discussing hash tables, discusses the Birthday Paradox.
Now, I’d never heard of it before. But sure enough, when presented with the problem of “In a room of 23 people, what are the chances that any two would have the same birthday?” my mind took the exact same intuitive decision making steps that most folks would.
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The answer is 50%.
After reading another math explanation on why that’s true, I know that I understand it now. Sure, I might not be able to repeat (or fully understand) the math equations which generate the percentage, but I can identify the bottom line of understanding — when written in POE (plain ol’ English):
The actual birthday problem asks whether any of the 23 people have a matching birthday with any of the others — not one in particular. That means, you aren’t just taking any two people and comparing their birthdays, but simultaneously comparing all possible pairings of the group.
It’s not the intuitive way to think of the problem. Your brain wants to tackle the problem it’s given of comparing two things, rather than the mathematical way which says “what are the chances that 23 people don’t share the same birthday”.