I know this problem is negative binomial, but I'm having problems on trying to set it up. Any help would be greatly appreciated.
A family decides to have children until they have three boys. Assuming that the probability of having a girl is 0.5 per birth and that the gender of each child is not influenced by the other children in the family, find the probability mass function of the random variable X = number of children in the family. Next solve the same problem where instead of having children until they have three boys the family stops when they have the third child of the same gender.