# Awesome Birthday Paradox

#### Simgar988

##### macrumors 65816
Original poster
365/2= 182?

90?

70?

Actually, the answer is 23 people. For a 99% chance the answer is 57 people.

VERY INTERESTING AND COUNTER-INTUITIVE!
http://en.m.wikipedia.org/wiki/Birthday_problem?wasRedirected=true

lets test! no cheating please!

September 10

For simplicity, disregard variations in the distribution, such as leap years, twins, seasonal or weekday variations, and assume that the 365 possible birthdays are equally likely. Real-life birthday distributions are not uniform since not all dates are equally likely

#### sycho

##### macrumors 6502a
Novermber 22nd.

I love the Birthday Paradox.

#### Simgar988

##### macrumors 65816
Original poster
so do I but I guess no one else does lol.

January 12.

#### OzExige

##### macrumors 6502
Why - yes, yes I do

huh?

oh

March 16th

##### macrumors 604
My 2 best friends and my girlfriend all have the same birthday as me... go figure.

#### flopticalcube

##### macrumors G4
My 2 best friends and my girlfriend all have the same birthday as me... go figure.
That must make for one heckuva birthday party.

My eldest son has my late mother's birthday and my middle child has my brother's. My wife shares hers with Hitler... I'm not going to add anything to that.

#### diamond3

##### macrumors 6502a
I'm more interested in how you do the stats for that problem. I should remember, but i had a terrible teacher and it has been a few years.

2/26

#### jhero

##### macrumors 6502
I'm more interested in how you do the stats for that problem. I should remember, but i had a terrible teacher and it has been a few years.

2/26
Agreed. The stats would be very interesting to see.

10/21

#### bgd

##### macrumors regular
365/2= 182?
Real-life birthday distributions are not uniform since not all dates are equally likely[/SIZE]
And why is this? Time of year, more kids conceived in winter for example?

Remember a story about a powercut in Britain leading to a spike in births nine months down the track.

So what sort of things make some dates less likely than others?

01/26

#### Counterfit

##### macrumors G3
My paternal grandmother was born exactly one year after (before maybe? I forget who's older) one of her sisters, on Valentine's Day. Pretty neat.

Then, she not only had one kid on her birthday, but two, also exactly one year apart. And just this past June, my sister-in-law gave birth on her birthday. So in my family, it's pretty damn likely.

#### swiftaw

##### macrumors 603
Ok, if you have n people then there are 365^n different ways they could have birthdays.

Of those ways, 365! / (365-n)! of them are such that everyone has a unique birthday.

Now, under some simplifying assumptions (no leap years, uniform distribution of births over all days) the probability that a group of n people all have unique birthdays is [365! / (365-n)!] / [365^n]. Therefore, the probability that at least two people share a birthday is

1 - [365! / (365-n)!] / [365^n]

If you plug in n=23, the answer is around 50%, the bigger n is, the higher the probability (obviously).

#### yg17

##### macrumors G5
My wife shares hers with Hitler... I'm not going to add anything to that.
Hmm, I thought I was bad, I share my birthday with that bigoted bitch Anita Bryant.

May 14th.

#### 0098386

##### Suspended
I shared a birthday with a friend at college. We were really similar too; had the same humour, same hobbies, same weird twisted mind. Jan 8th.
I think I share a birthday with my great grandmother too. Who also died on the day my brother was born.

#### pit29

##### macrumors 6502a
Hey mine too- March 22
Same here! But I guess now this thread is biased...

#### Ttownbeast

##### macrumors 65816
And why is this? Time of year, more kids conceived in winter for example?

Remember a story about a powercut in Britain leading to a spike in births nine months down the track.

So what sort of things make some dates less likely than others?
One of the biggest conception times coincides with the start of the new school year here around the end of August, or beginning of September resulting in lots of May/June babies.

#### Doctor Q

Staff member
Hey mine too- March 22
By my count it took us only 10 people, not 23, to get a birthday match (March 22, between fireshot91 and pit29). The odds were good that it wouldn't take more than a forum page, and we beat even those odds!

Please don't post more birthdays in this thread. You are welcome to talk about this or other surprising facts of probability and math.

#### renewed

##### macrumors 68040
Just a fun fact I'm sure many of you know, but it's interesting nonetheless. If you go to the main Mac Forums page and scroll all the way down, you can see all the birthdays for that day. It's crazy how many members have the same birthday on any given day.

#### Roric

##### macrumors regular
At lunch today someone mentioned that they knew someone who was born on his dad's 30th birthday... and his own child is due to be born about 6 days after his 30th. Just think if the baby decides to come 6 days early. Three generations exactly 30 years apart from each other.

#### fireshot91

##### macrumors 601
Happy Birthday?

3/22
I didn't mention this before (For the sake of another person getting another birthday as me), but my mom's birthday is also the same day.