don’t know why but if i try to explain why i don’t get this paradox the post gets removed
In: 0
[https://www.scientificamerican.com/article/bring-science-home-probability-birthday-paradox](https://www.scientificamerican.com/article/bring-science-home-probability-birthday-paradox)
>Have you ever noticed how sometimes what seems logical turns out to be proved false with a little math? For instance, how many people do you think it would take to survey, on average, to find two people who share the same birthday? Due to probability, sometimes an event is more likely to occur than we believe it to. In this case, if you survey a random group of just 23 people there is actually about a 50–50 chance that two of them will have the same birthday. This is known as the birthday paradox.
We can work out the odds that nobody in a group shares a birthday – i.e. they all have different birthdays.
If we ignore February 29th (which is a complication that makes very little difference), then:
* All possible dates work for person 1. Probability that it works is therefore 1
* For person 2, they cannot have the same birthday as person 1. There are therefore 364 days that work out of the 365 in a year. Odds of this are 364/365. Total odds are 1 * 364/365.
* For person 3, they cannot have the same birthday as person 1 or person 2. There are therefore 363 days that work out of the 365 in a year. Odds of this are 363/365. Total odds are 1* 364/365 * 363/365. We can refactorise this as (365*364*363)/365^(3)
* I’m sure you can spot the pattern here. For n people, we have (365*364*…*(366-n))/365^(n)
* For n=23, this number is less than 0.5 (it is 0.493), meaning that it is more likely than not that two people do in fact share a birthday for groups of 23 or more people.
Latest Answers