RE: What's the probability that 3 out of 23 people will share the same birthday?
February 16, 2022 at 12:15 am
(This post was last modified: February 16, 2022 at 12:17 am by Paleophyte.)
(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.
