An urn contains 3333 marbles : 2001 black,999 white and 333 red.
You are requested to draw randomly a pair of marbles and to obey the following rules:
If none of them is red - discard both of them.
If only one of the marbles is red – discard the non-red marble and return the red one to the urn.
If both are red - discard both of them.

Continue drawing pair by pair and discarding as told until there is only a single marble left.

What is the probability of the last one being red?

Clearly the individual black and white don't matter, but we note that 3000 non-red marbles.  Then we consider what happens to the number of red marbles in each case:

If none is red - discard both of them.  Red unchanged.
If one is red - return it to the urn.  Red unchanged.
If both are red - discard both.  Red reduced by 2.

Since we start with an odd number of red marbles and the total can only go down by two, we will always end up with a single red marble.

So the answer to the question is 1.

Posted by Jer on 2012-05-01 12:11:34