- It's My Birthday
- Probability using combinatorics
- Find out what was Number 1 on your 14th birthday and why it matters

## It's My Birthday

Just for fun, we punched in the 14th birthdays of some music stars to see which song supposedly defines them best. We use cookies to make sure Official Charts is the Number 1 chart site on the web.

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By Rob Copsey Twitter. Kanye West — Stronger Harder, better, faster, stronger I'll just call it the probability that someone shares.

I'll call it the probability of sharing, probability of s. This is going to be 1 minus p of s. Or if we said that this is the probability-- or another way we could say it, actually this is the best way to think about it.

If this is different, so this is the probability of different birthdays. This is the probability that all 30 people have 30 different birthdays. No one shares with anyone. The probability that someone shares with someone else plus the probability that no one shares with anyone-- they all have distinct birthdays-- that's got to be equal to 1.

Because we're either going to be in this situation or we're going to be in that situation. So if we figure out the probability that everyone has the same birthday we could subtract it from We could we just rewrite this.

And the reason why I'm doing that is because as I started off in the video, this is kind of hard to figure out. You know, I can figure out the probability that 2 people have the same birthday, 5 people, and it becomes very confusing. But here, if I wanted to just figure out the probability that everyone has a distinct birthday, it's actually a much easier probability to solve for.

So what's the probability that everyone has a distinct birthday? So let's think about it. Just for simplicity, let's imagine the case that we only have 2 people in the room.

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What's the probably that they have different birthdays? Let's see, person one, their birthday could be days out of days of the year.

### Probability using combinatorics

You know, whenever their birthday is. And then person two, if we wanted to ensure that they don't have the same birthday, how many days could person two be born on? Well, it could be born on any day that person one was not born on. So there are possibilities out So if you had 2 people, the probability that no one is born on the same birthday-- this is just 1.

Now what happens if we had 3 people? So first of all the first person could be born on any day. Then the second person could be born on possible days out of And then the third person, what's the probability that the third person isn't born on either of these people birthdays? You multiply them out.

You get times actually I should rewrite this one. Instead of saying this is 1, let me write this as-- the numerator is times over squared. Because I want you to see the pattern. Here the probability is times times over to the third power.

## Find out what was Number 1 on your 14th birthday and why it matters

And so, in general, if you just kept doing this to 30, if I just kept this process for 30 people-- the probability that no one shares the same birthday would be equal to times times I'll have 30 terms up here.

All the way down to what? All the way down to That'll actually be 30 terms divided by to the 30th power. And you can just type this into your calculator right now.

It'll take you a little time to type in 30 numbers, and you'll get the probability that no one shares the same birthday with anyone else. But before we do that let me just show you something that might make it a little bit easier. Is there any way that I can mathematically express this with factorials? Or that I could mathematically express this with factorials?

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