Xi'an's Og

An ex se intellegitur from The Fiddler

You are given an urn containing 100 balls. N of them are red, and 100−N green, where N is chosen uniformly at random between 0 and 100 (inclusive). You take a random ball out of the urn—it just so happens to be red—and discard it. Is the next ball you pick, from among the 99 remaining balls, more likely to be red or green?

since this is Bayes or Laplace in action. Namely, since P(R,R⁰|N)=N(N-1)/100×99 and

or

the probability is,

which is equal to  2/3 (for any total number of balls) since

n(n+1)(2n+1)/6-n(n+1)/2=n(n+1)(2n-2)/6

by a variation of Gauss formula. Once again ChatGPT³ got it all wrong:

This entry was posted on March 31, 2024 at 12:24 am and is filed under Books, Kids, pictures, Statistics with tags An Essay towards solving a Problem in the Doctrine of Chances, Bayes formula, Bayesian predictive, Carl Friedrich Gauss, ChatGPT, Laplace succession rule, riddle, The Fiddler. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.