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Awesome Birthday Paradox

Simgar988

Simgar988

macrumors 65816
Original poster
Jul 22, 2009
1,096
52
UYBAATC
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
 
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
 
Simgar988 said:
365/2= 182?
Real-life birthday distributions are not uniform since not all dates are equally likely[/SIZE]
Click to expand...

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?
 
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.
 
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).
 
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.
 
bgd said:
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?
Click to expand...

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.
 
comictimes said:
Hey mine too- March 22 :)
Click to expand...
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.
 
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.
 
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.
 
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