Probability that both 2 already born children are girls given that one of them is a girl Question:You have asked a woman if she has any children. She answered that she has two children. Then you have asked her whether if she has daughter out of those two. She said yes. What is the probability that both of her child are girls?

One answered 1/3 because one thinks that there are 3 outcomes:

boy and girl

girl and boy

girl and girl

What is the correct answer?
And if you think the answer isn't 1/3, how do you explain that the above explanation is wrong?
you are quite right, $S=\{gg, gb,bg\}$(since she has said she has atleast one girl then bb doesnt happen,both are girls =$A=\{gg\}$ thus answer is $p(A)=\frac{n(A)}{n(S)}=\frac{1}{3}$.
Your answer is correct. You can also work it out using the formula for conditional probability:

\begin{eqnarray}
P(\textrm{two girls}\ |\ \textrm{at least one is a girl}) &amp; = &amp; \frac{P(\textrm{two girls } \textbf{and} \textrm{ at least one is a girl})}{ P(\textrm{at least one girl})} \\
&amp; = &amp; \frac{\frac{\left|\{GG\}\right|}{\left|\{BB, BG, GB, GG\}\right|}}{\frac{\left|\{GB, BG, GG\}\right|}{\left|\{BB, BG, GB, GG\}\right|}}\\
&amp; = &amp; \frac{\frac{1}{4}}{\frac{3}{4}} \\
&amp; = &amp; \frac{1}{3}
\end{eqnarray}