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?

I used excel to calculate how many times I would expect to get all 100 white marbles, for each quantity of white marbles in the jar.  

For 100, it's 100, for 99 white marbles, it's 36.6 times, 98 white marbles, it's 13.3, etc.

When you add it all up, you get 157.211406637055 times.  My guess, therefore, is that out of every 157.21 times you get all 100 white marbles, 100 of those times it was because they were all white in the jar, so my guess is that it's 100/157.21......, or a 63.6086160280115% chance.

Anyone else?

Posted by Ryan on 2006-05-18 13:07:54