A family has 2 children and you know that the first child is a girl. What is the likelihood that the second one is also a girl?
This and many variations of this are very commonly asked questions in an interview setting. As we explain in detail later in Question
6.12, this type of question provides seemingly irrelevant prior information that affects our posterior estimates. Instead of solving this formulaically, we can just write down the possible combinations given that
the first child is a girl:
GG, GB
Hence, the chance that the second child is also a girl is 1/2.
If we didn’t have the prior evidence and the question was what is the likelihood that both children are girls, the chances would have been 1/4. If we now knew that
one of the children is a girl but didn’t know which one, the chances of the other child being a girl would have been 1/3. You can explore such variations at
https://www.madinterview.com.