So the birthday paradox is where if you’re in a room with 23 other people there’s a 50% chance of at least two people having the same birthday. Alternatively, In a room of 75 there’s a 99.9% chance of at least two people matching.
Why is this?
In: 134
Here are some statistics I derived using a Matlab script for this paradox:
With a group of 1 there is a 0% chance.
With a group of 15 there is a 25% chance.
With a group of 23 there is a 50% chance.
With a group of 50 there is a 97% chance.
With a group of 69 there is a 99.9% chance.
🙂
Why wouldn’t it be 1/365? Or does it have more to do with human mating schedules?
If it’s JUST TWO people in a room, there is a 1:365 chance they have the same birth day. You have ONE chance to match birth days.
If there are THREE people in the room, there is a 1:365 chance first person has the same birth day as the 2nd person. There is a 1:365 chance they have the same birth day as the second person. There is a 1:365 chance that the second person matches the third person.
Adding ONE PERSON means that there are THREE times as many chances to hit that rare probability and its 1:365 + 1:365 + 1:365 not 3:365 (these are very different in probability)
If you add a 4th person your have 12 chances for the probability.
If you add a 5th person you have 20 chances for a match
6th person 30 chances for a match
7th person 42 chances
It’s not an actual paradox, it’s just something that is counter intuitive. Others have it explained it well, I just wanted to add that definition though.
The reason the number is so low compared to what one might expect is because the instinctive way people think of this is usually “How many people would I need to have in a room before one of them had my birthday?” even if they don’t neccesarily think those exact words in their head. That’s a different question. What we want to know is how likely is it that ANY two people match birthdays.
So when you have two people in a room there’s two people that both have a 1/365 shot. With three people you have three people who each have a 2/365 shot and so on. So with 23 people each of them has a 22/365 shot. That ends up with 254 unique combinations.
254 tries at a 1/365 suddenly doesn’t seem like such long odds
There are already good explanations for the math behind the probability, but it’s worth noting that this assumes that births are distributed flatly throughout the year, which isn’t really true.
This just isn’t possible, I know people like to use fancy math to make it sound good, but it just doesn’t work like that. There’s a website that generates random numbers. I set it to pick 23 numbers at random between 1 and 365. I have yet to have two matching numbers in any example. The math just doesn’t work out.
Numbergenerator.org set to allow duplicates, and sort. Been close, but so far no matches after about a dozen rolls.
oh so the odds are of any two people having the same birthday. I once made a bet with my dad for $100 that someone in a small theater (75 or so people) would have the same birthday as him. I won the bet, but it appears i just got lucky lol
I used to be a cashier in college at a Walmart and there was this one guy that would go through my line to purchase alcohol. I once made the comment while checking his ID that we had the exact same birthday. It was the same day, month and year. I hope my birthday twin is living his best life right now.
Another way to think about this is to imagine a dart board cut into 365 slices. You start throwing darts. The birthday paradox tells you that by the time you throw your 23rd dart, there’s a 50% chance that you’ll have hit the same segment twice.
The chance of hitting a unique segment every time for 75 throws is less than 1%, which gives the second bit.
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