# Card drawing probability

#### CameronNY

##### New Member
Hey all, I have been pondering about a problem in excel and cant seem to figure it out :/

Lets assume I have a card deck of 50 cards. My opening hand is 5 cards, and I want to calculate my chance of drawing at least 1 red and at least 1 blue.
N total = 50
N blue= 10
N red = 5
N others = 35

How would I go about this? I am using the HYPGEOMDIST function to find my probablity of drawing at least 1 blue. But I cant just multiply this number with the probablity of drawing at least 1 red to arrive at my answer, right?

#### katxt

##### Member
HYPGEOMDIST applies to two choices without replacement. This is three choices without replacement.
If you are wanting to use Excel, I suggest =COMBIN(n,r). List the possibilities of at least one of each of R and B. There are 10 of them RRRRB, etc RRBOO etc through to RBBBB. Imagine the cards in three piles and you need to find how many RRBOO hands there are. There will be COMBIN(5,2)*COMBIN(10,1)*COMBIN(35,2) = 133875 RRBOO hands. Find the total for all 10 types. This can be done quickly if you have set things out well in a table. The total number of possible hands is COMBIN(50,5). The fraction will give you the probability (between 25% and 30%).

#### Buckeye

##### Member
HYPGEOMDIST applies to two choices without replacement. This is three choices without replacement.
If you are wanting to use Excel, I suggest =COMBIN(n,r). List the possibilities of at least one of each of R and B. There are 10 of them RRRRB, etc RRBOO etc through to RBBBB. Imagine the cards in three piles and you need to find how many RRBOO hands there are. There will be COMBIN(5,2)*COMBIN(10,1)*COMBIN(35,2) = 133875 RRBOO hands. Find the total for all 10 types. This can be done quickly if you have set things out well in a table. The total number of possible hands is COMBIN(50,5). The fraction will give you the probability (between 25% and 30%).
I have a question. Would it not be easier to find the probability of no red and no blue cards. Then use the complement to find the desired probability?

I think I see the mistake in my reasoning, not(not red and not blue) would be at least one red or at least one blue. Additionally, we could use the multivariate hypergeometric?

Last edited:

#### katxt

##### Member
Multivariate hypergeometric lets you find the probability of a specific exact combination. The "at least" part means that you will have to sum some things anyway.
Post back if you want to see a spreadsheet. kat

#### CameronNY

##### New Member
HYPGEOMDIST applies to two choices without replacement. This is three choices without replacement.
If you are wanting to use Excel, I suggest =COMBIN(n,r). List the possibilities of at least one of each of R and B. There are 10 of them RRRRB, etc RRBOO etc through to RBBBB. Imagine the cards in three piles and you need to find how many RRBOO hands there are. There will be COMBIN(5,2)*COMBIN(10,1)*COMBIN(35,2) = 133875 RRBOO hands. Find the total for all 10 types. This can be done quickly if you have set things out well in a table. The total number of possible hands is COMBIN(50,5). The fraction will give you the probability (between 25% and 30%).
Thank you very much, kat!