Question

Do more than 50 percent of the children in a certain group have brown hair?

(1) 70 percent of the boys in the group have brown hair.
(2) 30 percent of the children in the group are girls with brown hair.

Answer 1

What we know is that 30% of the group have brown hair and are girls. It means that in the other 70% we have the boys with brown hair, the other boys and the other girls.

In the case all the girls have brown hair, the 70% remaining would be boys. So 70% of then would have brown hair. (0.7*0.7=0.49 -> 49% of the children would be brown hair) so 49% (boys) and 30% (girls) are more than 50%..

Now, let's suppouse that 90% of the group are girls. It means 10% are boys and 70% of that 10% (=7%) are the boys in the group that have brown hair. Now 7% + 30% of the children have brown hair, wich isn't more than the half.

We have explained with two extreme cases that the information is not enough for making a precise answer