Communities

Writing
Writing
Codidact Meta
Codidact Meta
The Great Outdoors
The Great Outdoors
Photography & Video
Photography & Video
Scientific Speculation
Scientific Speculation
Cooking
Cooking
Electrical Engineering
Electrical Engineering
Judaism
Judaism
Languages & Linguistics
Languages & Linguistics
Software Development
Software Development
Mathematics
Mathematics
Christianity
Christianity
Code Golf
Code Golf
Music
Music
Physics
Physics
Linux Systems
Linux Systems
Power Users
Power Users
Tabletop RPGs
Tabletop RPGs
tag:snake search within a tag
answers:0 unanswered questions
user:xxxx search by author id
score:0.5 posts with 0.5+ score
"snake oil" exact phrase
votes:4 posts with 4+ votes
created:<1w created < 1 week ago
post_type:xxxx type of post
Search help
Notifications
Mark all as read See all your notifications »
Q&A

Why shouldn't the Bose-Einstein value be used to calculate birthday probabilities?

+0
−3

Can you please expound and simplify the embolden phrase below?

As another example, with n = 365 days in a year and k people, how many possible unordered birthday lists are there? For example, for k = 3, we want to count lists like (May 1, March 31, April 11), where all permutations are considered equivalent. We can't do a simple adjustment for overcounting such as $\dfrac{n^k}{3!}$ since, e.g., there are 6 permutations of (May 1, March 31, April 11) but only 3 permutations of (March 31, March 31, April 11). By Bose-Einstein, the number of lists is $\dbinom{n+k-1}{k}$. But the ordered birthday lists are equally likely, not the unordered lists [Emphasis mine], so the Bose-Einstein value should not be used in calculating birthday probabilities. $\square$

Blitzstein. Introduction to Probability (2019 2 ed). p 20.

Why does this post require moderator attention?
You might want to add some details to your flag.
Why should this post be closed?

0 comment threads

0 answers

Sign up to answer this question »

This community is part of the Codidact network. We have other communities too — take a look!

You can also join us in chat!

Want to advertise this community? Use our templates!

Like what we're doing? Support us! Donate