# Confusing Probability?

+1 vote
218 views

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 ?

posted Jan 26, 2015

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

answer Jan 26, 2015

Similar Puzzles

It is given that in a group of 5 Executives in an organisation, the probability of 3 of them not having the same birthday is 0.962.
What is the probability that the 3 Executives have the same birthday?

There are two bags.
First contains 7 red and 5 violet balls whereas second contains 7 violet and 5 red balls.
A ball is drawn at random from both the bags.
What is the probability of both balls having same colour?

+1 vote

Tickets numbered 1 to 37 are mixed up and then a ticket is drawn at random.
What is the probability that the ticket drawn has a number which is a multiple of 4 or 10?