(multivariate?) Hyper Geometric Distribution / excel

Hi everyone,

I'm working on a problem related to Hyper Geometric Distribution; I searched the forum and found a number of posts related to it in this "advanced statistics" forum but wasn't able to find a specific thread that helps..

Let's say I have a standard playing card deck (52 cards) and am looking for the odds of: **In the first 15 cards I draw, finding at least 1 King *and* at least 1 Queen.**

I'm using Excel rather than have to do this by hand, so for finding a King in the first 15 cards, I have:

=1-(HYPGEOMDIST(0,15,4,52)) - which gives me ~75.6%

0 = finding none

15 = sample

4 = successes

52 = population

The odds of finding BOTH in a 15 card sequence would be roughly 0.756 squared, or 57.16%, but obviously if I draw a King in the first 15 cards, that will decrease the odds of drawing a queen. Over a small example like this one, the difference is probably negligible, but I'd like to get an idea how to calculate this for more precision on larger (and more important) problems.

Any help - either relating to how to solve this mathematically or how to bend Excel to my will - is much appreciated!

-Bort

Re: (multivariate?) Hyper Geometric Distribution / excel

Quote:

Originally Posted by

**bortsampson** I'm working on a problem related to Hyper Geometric Distribution; I searched the forum and found a number of posts related to it in this "advanced statistics" forum but wasn't able to find a specific thread that helps..

Let's say I have a standard playing card deck (52 cards) and am looking for the odds of: **In the first 15 cards I draw, finding at least 1 King *and* at least 1 Queen.**

Let $\displaystyle K$ be the event that **no kings** are among the first fifteen drawn.

Let $\displaystyle Q$ be the event that **no queens **are among the first fifteen drawn.

If you can find $\displaystyle 1-\mathcal{P}(K\cup Q)$ you have it.