Hi! We are glad that you posted here! This looks like a homework question though. Our homework help policy can be found here. We mainly just want to see what you have tried so far and that you have put some effort into the problem. I would also suggest checking out this thread for some guidelines on smart posting behavior that can help you get answers that are better much more quickly.

I don't have emotions and sometimes that makes me very sad.

I'm 36 and a director of my own business in the UK. I've taken a real world question and anonymised it so that people can't infer what i'm actually looking which is an issue of corruption in my business.

I'll give it a go though...

On drawing 1 ball the probability of it being a green ball is (4/13)*100. The probability of it NOT being a red ball is (11/13)*100.
On drawing a 2nd ball the probability is conditional on what happened in the 1st draw so i'm guessing it's some kind of series of multiplications of these probabilities.

this is the formula (Multivariate hypergeometric distribution)

The mathematical explanation of a statistical procedure is really just pseudo-code, which we can make operational by translating it into real computer code. --B. Klemens

The answer isn't too hard to get but the little details you told us about your actual problem make me think that the probability question you provided won't actual get at the entire question you actually have. Of course I can't know that for sure without having more information about your *actual* question though. If you can't post it publicly maybe if you sent me a PM I could make it more anonymous for you if you want and help you along from there.

I don't have emotions and sometimes that makes me very sad.

Without having to derive the conditional probabilities we know this is the correct formula because the multivariate hypergeometric probability function is the formula to use when sampling without replacement from more than 2 groups. R code below.

Code:

# R code:
# multivariate hypergeometric for
# 3 classes: green, red, black
# caps = population total
# small = sample
mh = function(G,R,B,g,r,b){
choose(G,g)*choose(R,r)*choose(B,b)/choose(G+R+B,g+r+b)
}
mh(5,10,15,2,2,2) # wikipedia example -- 0.0795756
mh(4,2,7,3,0,5) # your example -- 0.06526807

The mathematical explanation of a statistical procedure is really just pseudo-code, which we can make operational by translating it into real computer code. --B. Klemens