You have a jar that is filled with a hundred marbles, each of them either black or white, but you have no idea how many of each color there are. However, you have been told that all possible quantities of white marbles (from 0 to 100, both inclusive) are equally probable.

You randomly select 100 marbles from the jar one at a time, with replacement, and they are all white. What is the probability that the jar contains only white marbles?

In this situation:
(probability of having all whites given a sample of 100 whites )X
(probability of sample of 100 whites) =
(probability of a sample of 100 whites given having all whites)X
(probability of having all whites)
P(All W | 100 w) is what we want.
P(100 w) is the summation sigma((1/101)*(k/100)^100,k=0,100)
P(All W) is 1/101
P(100 w | All W) is 1.

Simplifying P(A W | 100 w)=1/(sigma((k/100)^100,k=0,100) which is approximately .63, which is in agreement with Ryan's and Charlie's results.

Edited on May 18, 2006, 1:47 pm

Posted by owl on 2006-05-18 13:45:44