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Why, in a group of 23 people, will two usually share a birthday?

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alarcojon Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Nov-12-05 06:16 PM
Original message
Why, in a group of 23 people, will two usually share a birthday?
Don't believe me? Try it a few times.
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Chan790 Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Nov-12-05 06:28 PM
Response to Original message
1. I've never met anybody that shares my birthday
and I know a lot of people.
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alarcojon Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Nov-12-05 06:36 PM
Response to Reply #1
3. Different question
I didn't ask what are the chances someone shared a birthday WITH YOU - rather what are the chances some two people share a birthday.

If you ask 23 people at random for their birthday, there is a better than 50/50 chance that two of them will have the same birthday, but a pretty low chance that they will share YOUR birthday.
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Chan790 Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Nov-12-05 06:39 PM
Response to Reply #3
5. Oh I got that
I was making the offhand comment that it's never my birthday.
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aePrime Donating Member (676 posts) Send PM | Profile | Ignore Sat Nov-12-05 06:42 PM
Response to Reply #5
6. If you stopped claiming your birthday
was in Octovemarche this might not be a problem. That's not a real month you know.
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Chan790 Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Nov-12-05 06:49 PM
Response to Reply #6
12. Geez, get it right
It's Janutemberpril 33rd. :)
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alarcojon Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Nov-12-05 06:42 PM
Response to Reply #5
7. Sorry, didn't mean to suggest otherwise
It does seem odd you've never met someone with your b'day.
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momophile Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Nov-12-05 06:33 PM
Response to Original message
2. crazy, huh
I was in a group of 27 and there were two pairs that shared birthdays. Weird.
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aePrime Donating Member (676 posts) Send PM | Profile | Ignore Sat Nov-12-05 06:39 PM
Response to Original message
4. Because
If we look at the probability that no two people of the 23 share a birthday, each person can celebrate his/her birthday on any one of the 365 days (ignoring Feb 29), leading to 365^23 outcomes. Assuming each outcome is equally likely, the probability is 365 * 364 * 363 * ... * (365 - 23 + 1) / 365^23. This probability is less than 1/2, meaning that the probability that two of these people share the same birthday is greater than 1/2.

Sure, it makes sense mathematically, but it's still fun to use as a bet when you have a group of 23 or more people together.
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trof Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Nov-12-05 06:43 PM
Response to Reply #4
8. I thought it was "just" because.
But I could be wrong.
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aePrime Donating Member (676 posts) Send PM | Profile | Ignore Sat Nov-12-05 06:46 PM
Response to Reply #8
10. Brilliant!
You just wrote the majority of my dissertation.

I'll cite you, of course. :)
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alarcojon Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Nov-12-05 06:49 PM
Response to Reply #4
11. Absolutely
an easy way to make a dishonest buck, too. B-)

For example, in a group of 40 people, there is almost a 90% chance of a shared birthday.
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Gormy Cuss Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Nov-12-05 08:21 PM
Response to Reply #4
13. One of the "why math is fun" exercises I remember from junior high
Edited on Sat Nov-12-05 08:24 PM by Gormy Cuss
That was our introduction to the topic of probability.
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Kellanved Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Nov-12-05 06:46 PM
Response to Original message
9. The Illuminati
They even control probabilities.
:tinfoilhat:
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XemaSab Donating Member (1000+ posts) Send PM | Profile | Ignore Sat Nov-12-05 08:48 PM
Response to Original message
14. I narrowly escaped
sharing a birthday with W.... less than 3 hours....

:puke:
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