My cousin who is close to ten years younger than I am is getting ready to finish high school.

Now of course this will make more sense if you have some background, but since the math class that she was in had 23 students the teacher decided to given them The Birthday Problem, or Paradox as I learned it.

For those of you who don't know, it goes like this: In a room with 23 people there's a 50% chance that 2 people will have the same birthday. Which there was, but more on that later.

It makes more intuitive sense if you think about all the possible pairs instead of just the total number of people.

In a room with **23 people**, there are **253 (22 + 21 + 20 + ... + 1)** possible birthday pairs.

The equation is a bit complicated to derive, but it's based off the idea of first calculating the probability that all birthdays are different and subtracting that from 1.

That is to say, there are *366 possible birthdays* (including Feb 29). So the first person has a birthday, say Jan 1. The probability that the 2nd person's birthday is not Jan 1 is 365/366. The probability that the third person's birthday is not Jan 1 or the second birthday is 364/366. You do that as many times as people you have. When you multiply all those probabilities and subtract from 1, you get the probability that at least 2 people share a birthday, and when there are 23 people, that probability is roughly 50%.

This equation, however, assumes that all birthdays are equally probable, which we know isn't true.

Now, as it turned out there were two people with the **same birthday**. It is a girl that she is only acquainted with, and isn't really friends. But thanks to the problem, they did have a chance to connect.

And well, they hit it off.

Which, with teen girls, this means that they got to be good friends really quickly. I got the invitation in the main for "their" birthday party. I should clarify, I am practically like a big sister. When she was younger she spent a lot of her summer break at our home. And I took her with me when I went out on errands.

It was a nice invitation, perfect for teens, somethingt hat is really important when you celebrate a birthday at that age.

Either it is too babyish or it doesn't have the right look. They are hard to please.

It should be fun!