hi Mellie,
since when is a dart board square?
Anyway the area of the whole board is 4*4=16 cm squared. That will be the denominator.
the shaded area will be 3*3-2*2 = 9-4 = 5 cm squared.
So the prob that it will be in the sahaded region is $${\frac{{\mathtt{5}}}{{\mathtt{16}}}}$$
.