Confusing Probability?

Question

You along with your friend are standing in front of two houses. Each of those houses inhabits a family with two children.

Your friend tells you the below two facts:
1) On your left is a family that has a boy who likes accounts but the other child loves science.
2) On the right is a family with a seven year old boy and a new born baby.

You ask him, "Does either of the family have a girl?"

To this he replies, "I am not quite sure. But can you guess that? If you are right, I will give you $200."

Which family do you think is likely to have a girl ?

Answer 1

1/2 is the answer

In the house on the left, there are three possibilities:
Girl Boy
Boy Girl
Boy Boy

We cant have a girl-girl option because it has been mentioned that there is at least one boy in that house. Now all these outcomes are equally likely, and we have two events with girls, the chances of having a girl in the left house is 2/3.

In the house on the right, there are two possibilities because we already know that the older child is a boy:
Girl Boy
Boy Boy
Here the chances are 1/2.

Thus you must choose the house on the left for better chances at winning