Card probability - AAKK out of a deck

[bitwise]

@ultrafilter

Ask any mathematician how hard counting is, and he’ll tell you it’s frightfully difficult. That’s not widely known outside of our circle, so I can see where somebody might take offense, but none was meant.

Anyway, bitwise is using a generalized form of the hypergeometric distribution, which might be of interest to you. It makes problems like this quite simple.

I was? I vaguely remember that there was something called the hypergeometric distribution. It’s been a long time since I took probability. I explained my reasoning using counting methods above.

What is the generalized hypergeometric distribution? I found this

http://mathworld.wolfram.com/HypergeometricDistribution.html

and this

http://mathworld.wolfram.com/GeneralizedHypergeometricFunction.html

I can sort of see how you can generalize the hypergeometric distribution to a multivariate distribution. I have no idea how the second link is related.

[nivlac]

@Pullet

Then nivlac phrased it poorly.

That’s all. I don’t mean to pick a fight with anyone and I probably just over-reacted in my previous post.

Don’t want to hyjack the thread.

Yes, absolutely no insult of any kind intended in my original post. And I’m glad that fellow Dopers have jumped to my defense. When I teach this stuff (combinatorics), I always introduce the subject by saying that we will now learn how to count. The title of the chapter in the textbook is “counting techniques”. Then I go into examples to illustrate how difficult it is to count. Remember that probabilities are based on relative frequencies which is just a fancy way of saying dividing one count by another count. In the original question involving the probability of getting 2 aces and 2 kings when 4 cards are dealt from a 52 deck card, the answer is the ratio of the number of ways of getting 2 aces and 2 kings divided by the number of ways of getting 4-card hands. So you have know how to count to get the correct numerator and the denominator. Knowing combinatorics helps, but there are ways to reason it out as neuroman did.

[Thudlow_Boink]

@ultrafilter

Ask any mathematician how hard counting is, and he’ll tell you it’s frightfully difficult.

Okay, now I’m wondering:
Does The Count from Sesame Street know about permutations and combinations and all those complexities but he dumbs it down for the kiddies, or is he really not as great a count-er as he pretends to be?

[Pullet]

My appologies, nivlac, for being quick-tempered, but I’m glad y’all can see how I might take exception. Like I said before, I only know enough math to know I don’t know much, so I couldn’t appreciate the non-offensive qualities of your previous post.

Now that I’ve got my emotions under control, let’s get back to serious discussion.

The Count has, and always will be, a charlatan. A finishing school drop-out, the Count has had to build a career out of the one thing he did manage to learn, combinatorics. That, and he’s a jerk. He laughs everytime he’s counting because he realizes just how much he’s screwing up the little kiddie’s future math studies.

[ultrafilter]

@Thudlow Boink

Okay, now I’m wondering:
Does The Count from Sesame Street know about permutations and combinations and all those complexities but he dumbs it down for the kiddies, or is he really not as great a count-er as he pretends to be?

The Count is quite clearly a master of enumerative combinatorics.