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?

Will not the drawing of the first white marble on the first draw change the probability?  Does it not change to the possible sets from 101 (0 to 100 inclusive) to 100 (1 to 100 inclusive)?

Before any marbles are drawn, I can see the probability of the jar containing all white marbles being
1/101 * Sigma [x=0 to 100] x/100¹⁰⁰
= approx.  0.015721141

But, as it is given that at least one marble exists that is white, the probability of the jar containing all white marbles should be
1/100 * Sigma [x=1 to 100] x/100¹⁰⁰
= approx.  0.015812207

Or, if I am wrong here, please explain why.

Edited on May 19, 2006, 9:30 am

Posted by Dej Mar on 2006-05-18 16:54:47