davidd (davidd) wrote,

Happy Birthday(s)!

What are the chances that, of the, like, six or so people on my LJ friends list, two of them should have birthdays on precisely the same day?

Happy Birthday to zannah and pikachumustdie!!

They both happen to be among the most creative, intelligent, and witty people I've ever had the good fortune to know, in either cyber- or real life.

Hmmm... now I really am wondering; what are the chances?

Setting aside any seasonal variation in birth rates, the chances of somebody you meet having the same birthday as you are 1:365. That's easy enough.

But how do I figure the chances of any two people having the same birthdate? I've been teaching math, I should know this! It's a logic problem.

I believe it is correct to say that the chance that any two people have the same birthdays as each other would be 1:365.

So, if I have 6 people on my LJ list, the chance that any one of them would share a birthday with another of them would be 1:365 or 1:365 or 1:365 or 1:365 or 1:365... which equals 5:365, or 1:73. That's not particularly long odds, if I've figured this correctly. Maybe, then, it's not so amazing that two of my LJ acquaintances share a birthday.

But the chance that any specific two share a birthday would still be 1:365.

Now, what are the chances that a specific two share a birthday on a specific date? That is, if I name a date, what are the odds that two people will have a birthday on that day?

If I pick today, February 15, what are the chances it will be Zannah's birthday? Well, like, 100%, duh....! What I mean is, if I didn't know, and I picked a day at random, then the chances would be 1:365 that this was her birthday. Similarly, the chance that it would be Kendra's birthday would be 1:365. So the chance that I could pick a random day that just happened to be both Zannah's and Kendra's birthday would be 1:365 and 1:365, or 1/365 X 1/365, which is something like 1/133,225 (I used a Dashboard widget to figure that out -- first time I've used the Dashboard, woo hoo!).

But out of a group of six people, what are the chances any two would share a birthday on any random day I select? Would it be 1/73 (the chance that any of the six share a birthday) and 1/365 (the odds of picking somebody's birthday at random), which would be 1/73 X 1/365 = 1/26,646? Or would my chances of picking a correct day be 6 (people) divided into 365 (days), or 1/61; or, assuming at least two of the six people share a birthdate, 5/365 or 1/73? That would mean the odds that I could pick the day two people share as a birthday would be 1/73 X 1/73, or 1/5329.

So, what are the chances that two of my LJ contacts would have the same birthday? Somewhere between 1:73 and 1:133,225. I think.
Depends on how you want to define it, I guess. Look, I never got much beyond the colored marbles in a bag thing, okay?

Whatevers. The blinkie thing is cool, isn't it:

Happy Birthday to zannah and pikachumustdie!!

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