You have a standard pack of 52 playing cards. You then shuffle them and begin to draw out cards until you have three of a kind. What is the most likely number of cards drawn when this happens?
You then shuffle another pack of 52 playing cards into the pile. What happens to the expected number of cards now? (i.e. does it double / halve / stay the same?)
(In reply to re(2): I think I've got it. (No computer program used).
"You can only achieve a true 'three of a kind' hand by drawing between 5 and 14 cards."
So, why do you have a probability of getting the "3 of a kind" on the 15th card (of 0.0000002468)?