For a family, There are 5 possibilities in having 4 childrens
No Boy { G,G,G,G}
1 Boy { B,G,G,G}
2 Boys { B,B,G,G}
3 Boys { B,B,B,G}
all boys {B,B,B,B}
For a family to have at least one boy the probability is = 4/5
So we can expect 2000* $\frac{4}{5}$ = 1600 families to have atleast one boy.