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

THREE OF A KIND !!!!!!! by Dan)

Sure, if there were any mention of poker in the question then I'd jump on your train, but, reading carefully, there is no such requirement. Assuming that the draws are related to poker changes the question in a very substantial way, as then both the definition of success and the method of trial change. By this I mean that the goal of the probability changes (because you're now looking for three matching cards and no pair, as opposed to simply three matching cards) and the procedure involoved changes because in (standard) poker you have only five cards from which to draw your hand, but in the question there is no such restriction - with 12 cards being A,A,2,3,5,7,7,8,8,8,Q,K we have succeeded in matching the problem requirements - if you'd draw and discard though (especially if originally dealt the 2 Aces along with only one of the 8's) then you've only 5 of these - what if you'd thrown an eight at some point? There is no mention of thrown cards when drawing new ones, and in fact, none of the previous solutions included that as a mechanism involved in the problem.

So while you've solved an interesting problem, it unfortunately was not the one as stated (as written) or as intended (I'm willing to bet that Lewis is not a poker player).