This is a hypergeometric distribution problem. Population (N=50=W+B) is divided into two classes, W (W=20) and B (B=30). We calculate the probability of choosing w (w=2) white and b (b=5) black marbles. Hypergeometric probability gives P(W,B,w,b)=C(W,w)C(B,b)/(C(W+B,w+b) where C(n,r)=n!/(r!(n-r)!) the number of combinations of choosing r out of n objects.
Here P(20,30,2,5) =C(20,2)C(30,5)/(20+30, 2+5) =190*142506/99884400 =0.2710
Alternatively, doing the combinatorics way: #of ways to choose 2 from 20 =C(20,2) #of ways to choose 5 from 30=C(30,5) total #of ways = C(50,7) P(20,30,2,5)=C(20,2)*C(30,5)/C(50,7) =0.2710 as before.
A strong negative correlation example would be the hours spend watching TV and your grades. It shows a strong negative correlation because if you just watch TV and not study for an exam, your grades would most likely be low.
