Probability question
- From: Fred Krogh <fkrogh@xxxxxxxxxxxxxxxx>
- Date: Mon, 25 Sep 2006 10:08:35 -0700
While trying to make up a problem to show that the human brain isn't well wired for dealing with probabilities, I at least managed to show that this was the case for me!
A bag has 4 marbles, each is black or white. They were placed in the bag by flipping a perfect coin and putting a white marble in for heads and a black one for tails. You randomly take out marbles one at a time record whether it is white or black and put it back. Let P(i,j) denote the probability that the next marble you draw will be white given that so far you have seen i white marbles and j black ones. Thus P(1,0) = 8/15, P(0,1) = 7/15, P(k,k) = 1/2 for any k. What is the general form for P(i,j)?
If this is too easy allow more marbles in the bag and/or add some more colors.
Fred
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