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.
The problem is clearly addition, so we can rule out B and C. Associative property is the movement of the parentheses, whereas commutative property is the movement or reorganization of the numbers. The parentheses moved in this problem, so it is associative. I suggest reviewing these properites, they come in handy later and are good to know :)
