If Ned said it, probability is 1 that it is GG;
If Red said it, it is either BG, GB, or GG, probability is 1/3 it is GG
If Ted said it, you know the older child is G, probability is 1/2 it is GG
If Zed said it, you know the coin selected child is G. He mentions sex of other child (G) so probability of GG is 1
1/4*1+1/4*1/3+1/4*1/2+1/4*1=17/24 = probability that it is GG.