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What's the probability that 3 out of 23 people will share the same birthday?
#21
RE: What's the probability that 3 out of 23 people will share the same birthday?
(January 24, 2022 at 4:26 am)Abaddon_ire Wrote:
(January 24, 2022 at 2:06 am)FlatAssembler Wrote: So, where do you think the error lies? https://flatassembler.github.io/birthday_paradox.aec

The error is that you do not understand any of it. 

Is that clear enough?

Why do you think that I do not understand any of it? It's written in a programming language I made, so I understand precisely what each directive means. And it's an algorithm I made up, so I understand it as well.
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#22
RE: What's the probability that 3 out of 23 people will share the same birthday?
(January 24, 2022 at 2:06 am)FlatAssembler Wrote:
(January 22, 2022 at 7:02 am)BrianSoddingBoru4 Wrote: Your programme is flawed. If I enter '100' in the collisions field, the probability computes at 0%. This means that in a group of 23 people, there is no chance that they all share the same birthday. While such a coincidence is statistically unlikely, the probability is non-zero.

Boru
So, where do you think the error lies? https://flatassembler.github.io/birthday_paradox.aec

Fairly sure it’s a programmer error. 

Boru
‘Let me never fall into the vulgar mistake of dreaming that I am persecuted whenever I am contradicted.’ Ralph Waldo Emerson
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#23
RE: What's the probability that 3 out of 23 people will share the same birthday?
Wild guess. Probably to do with some limitation related to number of decimal places?

If the answer just keeps approaching 0 as you increase the input number, then inevitably you're going to get 0 as the answer with a very large input number like 100 because it can't handle too many decimal places.
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#24
RE: What's the probability that 3 out of 23 people will share the same birthday?
(January 24, 2022 at 11:01 am)GrandizerII Wrote: Wild guess. Probably to do with some limitation related to number of decimal places?

If the answer just keeps approaching 0 as you increase the input number, then inevitably you're going to get 0 as the answer with a very large input number like 100 because it can't handle too many decimal places.

Please tell me that handling too many decimals is a euphemism. Hehe
I don't have an anger problem, I have an idiot problem




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#25
RE: What's the probability that 3 out of 23 people will share the same birthday?
@polymath257 Perhaps you know the answer to this question?
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#26
RE: What's the probability that 3 out of 23 people will share the same birthday?
Personally, I blame hippies.
Dying to live, living to die.
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#27
RE: What's the probability that 3 out of 23 people will share the same birthday?
(February 13, 2022 at 11:07 am)FlatAssembler Wrote: @polymath257 Perhaps you know the answer to this question?

If there is not an analytic solution, then, there's an approximation, and certainly, a simulation.
And without delay Peter went quickly out of the synagogue (assembly) and went unto the house of Marcellus, where Simon lodged: and much people followed him...And Peter turned unto the people that followed him and said: Ye shall now see a great and marvellous wonder. And Peter seeing a great dog bound with a strong chain, went to him and loosed him, and when he was loosed the dog received a man's voice and said unto Peter: What dost thou bid me to do, thou servant of the unspeakable and living God? Peter said unto him: Go in and say unto Simon in the midst of his company: Peter saith unto thee, Come forth abroad, for thy sake am I come to Rome, thou wicked one and deceiver of simple souls. And immediately the dog ran and entered in, and rushed into the midst of them that were with Simon, and lifted up his forefeet and in a loud voice said: Thou Simon, Peter the servant of Christ who standeth at the door saith unto thee: Come forth abroad, for thy sake am I come to Rome, thou most wicked one and deceiver of simple souls. And when Simon heard it, and beheld the incredible sight, he lost the words wherewith he was deceiving them that stood by, and all of them were amazed. (The Acts of Peter, 9)
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#28
RE: What's the probability that 3 out of 23 people will share the same birthday?
The odds get way better in queue at the DMV...

Smile
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#29
RE: What's the probability that 3 out of 23 people will share the same birthday?
(January 21, 2022 at 2:06 am)FlatAssembler Wrote: 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.

As OLB alludes to above, there is insufficient information to answer this question. Nowhere does it say that these people are randomly selected. If you're in a neonatal unit then the odds that 3 of the 23 infants don't share a birthday are vanishingly small. Conversely, if you've carefully selected for two of each zodiac sign then you're nearly* guaranteed not to have more than two birthdays on any given day with low odds of even that.




For extra credit: You and 49 friends live in one of each of the 50 capitols of the states of the USA. Your birthdays are distributed randomly and you all visit the birthday boy(s) and/or girls(s) in their hometown on their birthday. What is the total minimum probabilistic travel distance for all of your friends in a year? Kindly do not ignore leap years, the curvature of the Earth, or that suspicious burning odour coming from your processor as you attempt to simulate this.
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