#### jensked

##### Well-Known Member

- Joined
- Mar 31, 2005

- Messages
- 4,053

When there are 26 (random) people in a bar, the chance that two of them share the same birthday, is 60%. That sound like bullshit, especially because there are 365 days and you are only with 26.

That's the beauty of the theory of probability.

What we are going to do, is to calculate the chance that nobody shares the same birthday. And then, we will distract (right term?) that chance from 100%.

Ok, here we go...

__Step one__

When there is only 1 person, the chance he does not share his birthday with anybody else is obviously

**365/365**.

When there is an extra 1 person, he can only have his birthday on the 364 other days. So the chance his birthday is on another day is

**364/365**.

When there enters a third person, the chance his birthday is on yet another day is

**363/365**.

...

You go on like that, and so the 26th person, has a

**340/365**chance his birthday is not on the same day as the others.

__Step two__

Now we can calculate the chance that nobody shares the same birthday.

In the theory of probability, you have to multiply the seperate chances.

so:

**365/365 x 364/365 x 363/365 x ... x 340/365 = 0.4 = 40%**

__Step three__

So now we know that the chance nobody shares their birthday is 40%.

So the chance that two people out of 26 share their birthdays is 60%.

crazy, isn't it?