Simple Birthday Probability Question

[Yeti]

In a group of 10 people what's the probability someone shares my birthday? Thanks.

[slickpoppa]

Assuming you weren't born on Feb. 29, the prob. is:
1 - (364/365.25)^10 = 3.37%

[jimdmcevoy]

However, if you wish to complicate things, you could take into account the fact that more people are born on certain days, for example Sept. 30 (champainge baby).

But I don't.

[La Brujita]

I am trying to relearn/reunderstand probabilities and I know the easiest way to do it is as slickpoppa did, subtrace the probability none share the same birthday from 1.

Just out of curiousity, and I don't need you all to spend any time actually doing it, would I be correct to assume it would be very hard to do it the long way by pen and paper?

How would you do it, compute the chance of exactly two having the same birthday, then exactly three etc?

Probably a basic question but it is what it is.

[slickpoppa]

The "long" way is as follows:
Chance of x people people having same birthday as you:
(1/365.25)^x * (364/365.25)^(10-x) * [10!/(x!*(10-x)!)]
Then you sum the above equation for x = 1,2,3,....

[La Brujita]

Thanks for this. I will have to think about it for a bit. You have a big brain!

[TomCollins]

This is not true if your birthday is Feb 29. /images/graemlins/smile.gif