*six*or so people on my LJ friends list, two of them should have birthdays on precisely the same day?

**zannah**

**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:

**zannah**

**pikachumustdie**