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 Some responses for SilverKnight,,,,
Dan, please go back and read my post AGAIN.
You wrote that:
52!/(50! * 2!) = (52*51)*2 = 5304
No, this is incorrect.
52!/(50! * 2!) = (52*51)/2 = 1326
And yes, Dan, I *do* think I can come up with that many different 2-card hands in a deck of 52.
Please forgive me for taking what you wrote LITERALLY. I simply thought that when you used the word 'only' that you meant 'only'. Silly me.
Did you take into account (I'm betting that you didn't...) the notion that you could get a straight or flush before you get your three of a kind? (The only reason I bring it up, is because you discounted getting a full house, in a previous post.)