A couple has two children. What is the probability that both are girls given that the oldest is a girl? What is the probability that both are girls given that one of them is a girl?
DO NOT assume that female births and male births are equally likely. Assume identical twins are necessarily the same sex.
Write your answer in terms of the probability of a female birth and the probability of identical twins (assume that identical twins are just as likely to be female as the overall female probability).
The Attempt at a Solution
All right the problem as stated in the first paragraph without extra stipulations is easy, but I am unsure about how to complete solution now. Considering the question "What is the probability that both are girls given that the oldest is a girl" , if we let A = event that both are girls and B = oldest is a girl. Then by Bayes,
P(A|B) = P(B|A)P(A) / P(B). But is this the correct way to go? Isn't P(B) just P(female birth)?