binomial distributions (family size)

particularly part B. Thanks!

A couple with two girls has decided to keep having children until they have exactly two
boys. The probability of a male birth is approximately 51%. Assume independence among
the genders of the children.
(a) Determine the probability that the couple will have at least two more girls before
completing their family.
(b) What is the expected size of such a family?


TS Contributor
Hi! Welcome to Talkstats! We are glad that you posted here! This looks like a homework question though. Our homework help policy can be found here. We mainly just want to see what you have tried so far and that you have put some effort into the problem. I would also suggest checking out this thread for some guidelines on smart posting behavior that can help you get answers that are better much more quickly.
I believe for part a), to have at least 2 more girls to complete the family by having additional 2 boys, we should have 1 or 0 boys in the coming 3 kids. Therefore, the probability would be .49^3+.51^2*.49*3=48.5%

For part b), since the family size could be unlimited if there are no boys (or just 1 boy) in the coming kids, I can calculate the expected family size. Kindly help to provide hint