A simple but confusing question

From: Shanyu Zhao (szhao_at_darkwing.uoregon.edu)
Date: 09/27/04 

Date: 27 Sep 2004 01:26:38 -0700

Hi,

Here is the naive question:

There are a large number of balls in a bucket, the white color balls
occupy p and the black balls (1-p). If p is unknown, when you pick 100
balls from the bucket, find that all of them are white. Then you pick
the 101st ball, what is the probability that the ball still a white
one?

If we can't calculate the probability, can we reach the conclusion
that the probability is greater than (100/101)? Or more precisely,
what is the bottom line of this probability. Intuitively it should be
above some value.

Is this problem a parameter estimation or hypothesis testing? If we
use parameter estimation, clearly p=1, which means the probability is
100%. But this is not true.

I've always been confused by this problem. Please help me out!
Thanks alot!

Shanyu

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