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?