Posts: 2020
Threads: 133
Joined: July 26, 2017
Reputation:
5
What's the probability that 3 out of 23 people will share the same birthday?
January 21, 2022 at 2:06 am
The probability that 2 out of 23 people will share the same birthday is slightly higher than 50%, and that is the famous Birthday Paradox. However, what is the probability that 3 out of 23 people will? I have, like I have written in this article about something distantly related to that, estimated numerically using Monte Carlo method that it is around 1.26%, and that the probability that 4 out of 23 people will share the same birthday is around 0.018%. However, I am interested whether there is a general formula for that.
Posts: 20476
Threads: 447
Joined: June 16, 2014
Reputation:
110
RE: What's the probability that 3 out of 23 people will share the same birthday?
January 21, 2022 at 2:33 am
(This post was last modified: January 21, 2022 at 2:34 am by ignoramus.)
ssssssss
No God, No fear.
Know God, Know fear.
Posts: 2020
Threads: 133
Joined: July 26, 2017
Reputation:
5
RE: What's the probability that 3 out of 23 people will share the same birthday?
January 21, 2022 at 4:57 am
(January 21, 2022 at 2:33 am)ignoramus Wrote: ssssssss
What does that mean?
Posts: 49754
Threads: 554
Joined: July 24, 2013
Reputation:
109
RE: What's the probability that 3 out of 23 people will share the same birthday?
January 21, 2022 at 5:09 am
It's one of those paradoxes that isn't. Here's the roughest way to look at it.
If you have a group of 23 people, the number of possible pairs is 253: 23x22/2. The odds of shared birthdays is found by dividing the possible pairs by the number of days in a year. 253/365 is just over 69% (the actual percentage is much closer to - but still above - 50%).
Boru
‘I can’t be having with this.’ - Esmeralda Weatherwax
Posts: 20476
Threads: 447
Joined: June 16, 2014
Reputation:
110
RE: What's the probability that 3 out of 23 people will share the same birthday?
January 21, 2022 at 5:26 am
(January 21, 2022 at 4:57 am)FlatAssembler Wrote: (January 21, 2022 at 2:33 am)ignoramus Wrote: ssssssss
What does that mean?
![[Image: giphy.gif]](https://media.giphy.com/media/ue5ZwFCaxy64M/giphy.gif)
No God, No fear.
Know God, Know fear.
Posts: 2020
Threads: 133
Joined: July 26, 2017
Reputation:
5
RE: What's the probability that 3 out of 23 people will share the same birthday?
January 21, 2022 at 5:44 am
(January 21, 2022 at 5:09 am)BrianSoddingBoru4 Wrote: It's one of those paradoxes that isn't. Here's the roughest way to look at it.
If you have a group of 23 people, the number of possible pairs is 253: 23x22/2. The odds of shared birthdays is found by dividing the possible pairs by the number of days in a year. 253/365 is just over 69% (the actual percentage is much closer to - but still above - 50%).
Boru
Right, it is more like the Monty Hall Problem: something which is not hard to analyze mathematically, but the result is surprising to most people.
Posts: 7259
Threads: 506
Joined: December 12, 2015
Reputation:
22
RE: What's the probability that 3 out of 23 people will share the same birthday?
January 21, 2022 at 6:32 am
(This post was last modified: January 21, 2022 at 6:45 am by Jehanne.)
Yes, there is a general formula, which can be reasoned as follows:
1) The probability of an event plus its complement (the event not occurring) is 1 (or, "unity").
2) While not being entirely true, we may assume, for convenience, that every day of the year is equally likely to be born on.
3) The probability of being born on any one day is 1/365 for non-leap years.
4) If a single person is born on one day, there are 364 other days for another individual to be born on, such that the two individuals do not have the same birthday. For the third individual, there would be 363 days, etc.
5) 1 - (365 * 364 * 363...) / 365 ^ n would give the probability that 2 or more individuals would have the same birthday.
P.S. Okay, it's 4 AM, and, so, I misread your question a bit. Yes, getting the probability for exactly three individuals is quite a bit more tricky.
Posts: 28873
Threads: 528
Joined: June 16, 2015
Reputation:
89
RE: What's the probability that 3 out of 23 people will share the same birthday?
January 21, 2022 at 8:49 am
I don't share my birthday with anybody, the cake is all mine damnit.
Being told you're delusional does not necessarily mean you're mental.
Posts: 18273
Threads: 143
Joined: July 10, 2013
Reputation:
65
RE: What's the probability that 3 out of 23 people will share the same birthday?
January 21, 2022 at 10:04 am
Another fascinating thread.
Send lawyers, guns, and money...
Posts: 2020
Threads: 133
Joined: July 26, 2017
Reputation:
5
RE: What's the probability that 3 out of 23 people will share the same birthday?
January 21, 2022 at 11:33 am
(This post was last modified: January 21, 2022 at 11:34 am by FlatAssembler.)
(January 21, 2022 at 8:49 am)brewer Wrote: I don't share my birthday with anybody, the cake is all mine damnit.
This is a serious question, and I do not expect joke answers.
(January 21, 2022 at 10:04 am)arewethereyet Wrote: Another fascinating thread.
Are you being serious or ironic, I cannot tell?
|
