# A deck of 52 cards is shuﬄed you are dealt 13 cards. X= # aces, Y= #spades. Show they are uncorrelated?

A deck of 52 cards is shuﬄed you are dealt 13 cards. Let X and Y denote, respectively, the number of aces and the number of spades in your hand. Show that X and Y are

uncorrelated.

### 1 Answer

- 7 years agoFavorite Answer
Ok, this sounds like a stats experiment and I have some doubt anyone else is willing to sound like an idiot trying to answer it.

So, we are using an experimental technique, at least in our minds, to deal 13 shuffled cards out of the deck. I can't word a logical proof that they're uncorrelated even though common sense says they're uncorrelated.

What I suspect is being asked of you is that you actually grab a deck of cards, shuffle it, and deal out 13 cards a bunch of times. Each time you deal, you record the number of aces, and the number of spades on a sheet of paper (like make three columns, one for the trial #, one for X/number of aces, and the last for Y/the number of spades). If you do this a number of times, you should find that the number of aces and spades do vary between iterations (each time you deal the cards is an iteration of the procedure), but the number of aces has nothing to do with the number of spades. Sometimes you get a few aces and a few spades; sometimes you get a few aces and a lot of spades; sometimes you get a lot of aces and a few spades; sometimes you get a lot of aces and a lot of spades. So lastly, if you take that data set you gathered and convert it to a graph and just mark the data points (1 ace with 3 spades would be the point (1,3), etc), you should find a giant confusing scattering of numbers, instead of a neat, straight line. That scattering means you have a correlation of close to 0. So, for this assignment, I think the teacher's expecting a data set, a graph, and the explanation of the correlation being 0 or close to 0. Just don't fudge the data, the dealing of cards is easy enough to do.

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