- Probability using combinatorics
- What's Your Number? The Vietnam War Selective Service Lottery | HistoryNet
- How Common is Your Birthday? This Visualization Might Surprise You
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Chart rival Rihanna b. 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. 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?
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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.
Probability using combinatorics
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? Let's think about it. You just keep multiplying. It's a huge number. Now, if I just want the times the in this case, I have to get rid of all of these numbers back here.
What's Your Number? The Vietnam War Selective Service Lottery | HistoryNet
One thing I could do is I could divide this thing by all of these numbers. So times all the way down to 1. So that's the same thing as dividing by factorial.
So this is equal to factorial over factorial over squared.
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And of course, for this case, it's almost silly to worry about the factorials, but it becomes useful once we have something larger than two terms up here.
So by the same logic, this right here is going to be equal to factorial over factorial over squared. And actually, just another interesting point. The song also peaked within the top ten of the charts in Australia, as well as the top 30 in Belgium, New Zealand and the Republic of Ireland.
The song was co-written with A. Rahman , composer of " Urvasi Urvasi ", from the soundtrack of Tamil Indian film Kadhalan , sampled in the song. Lewis Corner of Digital Spy gave the song a moderate review stating, saying: The video was credited to Interscope Productions and Maker Studios artists.
How Common is Your Birthday? This Visualization Might Surprise You
On July 21, the duo performed it with virtual body doubles on The Voice Australia , which was said to be "one of the biggest performances of the whole night". From Wikipedia, the free encyclopedia. For other uses, see It's My Birthday disambiguation. Rahman Keith Harris Cody Wise. Cody Wise — Single by will.
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