Alice has 2 kids and one of them is a girl. What is the probability that the other child is also a girl? (Apply Bayes' Theorem)

Question

I am aware that The outcomes for two kids can be {BB, BG, GB, GG}, and given that there's one girl, the answer would be 1/3. But, when I put the question into a context of Bayesian Theorem, I seem to struggle.

My equation is as follows: P(2G|1G)=[P(1G|2G)*P(2G)]/P(1G)

where P(1G|2G) = 1 as given there are two girls, the probability of having 1 girl would be 1, P(2G)=0.5*0.5, P(1G)=0.5 .

Where, in my equation, did I get wrong?

Answer 1

Your method is correct but you must remember that your P(1G) is the probability of at least one girl i.e. $3/4$.

Then your answer will be correct as well as your method!