The reason why the sum of your probabilities equals 0.5 is because you're only considering half of the problem--i.e. the probabilities for only one gender. For example, the probability that there are only three children and all are boys is 1/8. But, remember, it could be the case that there are three children and all are girls. Thus, the probability that there are three children is 1/4--not 1/8. Thus, multiply your result for P(X=4) and P(X=5) by 2 and you should end up with the right answer...