Question

A family decides to have children until it has three children of the same gender. Assuming P(B)=P(G)=.5,
what is the pmf of X = the number of children in the family?

This problem was in the section of negative binomial distribution in the textbook and i used the equation for nb but the sum of all the probabilities is just 0.5.
And, i saw in yahoo someone using the P(a)= N(a)/N and getting the sum of P(x)=1. Also, it made sense for this problem as both the events were equally likely-- P(B)=p(G)=0.5 .
But, shouldn't nb also give the same result as of using the classical definition?

Answer 1

And, yes this is not my homework question. This one is from the superset of questions for the quiz that we already had last week. And, this was also one of the questions on the quiz. And, she never gave us any answers for it.
I thought i did it right, but now i am preparing for a midterm that we have tomorrow. So, i wan't to make sure.

Answer 2

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...