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

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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 ?

pnikam Expert Asked on 22nd August 2015 in

This is a poorly stated problem.  The existing answer makes assumptions that aren’t stated, which result in the conclusion that the information about which child is older is relevant.  It’s not.

Let’s look at the problem another way.  In the house on the left, we have:

Accounts / Science
Boy Boy
Boy Girl

In the house on the right we have:

Younger / Older
Girl Boy
Boy Boy

With the given information, the odds are the same for either house to have a girl.

Consider a similar scenario with coins.  I flip two pennies and two dimes.  I tell you that the first dime flipped was heads and that the shinier penny is also heads.  In each case I’ve distinguished the two events–it doesn’t matter what I use to distinguish them, it only matters that they have been distinguished.

There is a more relevant piece of information revealed, which is that your friend is “not quite sure” if either family has a girl.  In order for this to be true, two things must be true: your friend does not know the gender of all four children and none of the children your friend does know about is a girl.  This leaves open the possibility that your friend knows the gender of one of the two other children (either the child that likes science or the baby), and that child is a boy.  Given that your friend knows that the other child in the house on the left likes science, I’m going to assume it is more likely that he also knows the gender of the second child in the house on the left, than the gender of the baby.  Based on THIS information, I pick the house on the right.

dougbell Genius Answered on 24th October 2015.

1/2

In the house on the left, there are three possibilities:
Younger Older
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:
Younger Older
Girl Boy
Boy Boy
Here the chances are 1/2.

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

anikam Expert Answered on 22nd August 2015.

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