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?)

First of all, I think this problem is a little beyond me, but I interpreted the problem to mean the probability of getting a three of a kind(non-poker) on drawing on a particular card. That means that you don't include the probability of already having drawn a three of a kind. Having a list of probabilities for each card makes it simple to calculate both anyway.

Second of all, to Dan,
You and other people have probably already told you this, but you take these puzzles too literally (or not literally enough, depending on how you look at it). I'm absolutely sure that yours was not the intended answer, and I think you know that, but pursue it anyway. Do you know how hard it is to write a puzzle that is free from problems that could be exploited by people like you? It takes very, careful phrasing.

Not that there's anything wrong with what you're doing, but the intended solution is what we're looking for, or a better one. By better, I mean things like a shorter proof.

Posted by Tristan on 2003-11-20 20:01:35