We remove $7$ without replacement. Let $R$ be the number of red balls removed and $B$ the number of blue balls removed. Do you expect $R$ and $B$ to be positively correlated, negatively correlated, or uncorrelated?
I feel like this should be a quick answer, but I'm just looking for some clarification on this problem. My professor's answers say "negatively correlated because more red balls in the sample means less blue balls in the sample". I was under the impression that if both $A$ and $B$ decreased/increased, they were positively correlated. Then for negative correlation, one had to go up, while the other went down, or vice versa.
It would be awesome if someone could enlighten me.
Thanks in advance!
If you choose $b$ blue balls, then you pick $7-b$ red balls. So $r=7-b$. So you have perfect negative correlation.