Negative binomial distribution - Wikipedia, the free encyclopedia,
just substitute r = 3 and p = 1/2: .
For Part II, let Y be the random variable number of children in family. Since the family stops when they have either 3 boys or 3 girls, Y can only have the values 3, 4 or 5:
(This corresponds to BBB or GGG)
(This corresponds to BGGG, GBGG, GGBG or GBBB, BGBB, BBGB)
(This corresponds to BBGGG, etc ...... or GGBBB, etc .......)