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

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.

• ## More puzzles to try-

• ### What is the logic behind these ?

3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »
• ### Five greedy pirates and gold coin distribution Puzzle

Five  puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »
• ### Defective stack of coins puzzle

There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »
• ### Dr. Willam and surgical gloves puzzle

Dr.Willam wants to operate for three different persons who were wounded. But he had only two surgical gloves. There is ...Read More »
• ### Which clock works best?

Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »
• ### To which one will the needle touch 1 OR 2

In the gear arrangement, To which one will the needle touch,  1 OR 2Read More »
• ### How did he know?

A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »
• ### Which letter replaces the question mark

Which letter replaces the question markRead More »
• ### Crossing the Bridge Puzzle (Bridge and torch problem)

A bridge will collapse in 17 minutes. 4 people want to cross it before it will collapse. It is a ...Read More »
• ### Probability of having boy

In a country where everyone wants a boy, each family continues having babies till they have a boy. After some ...Read More »
• ### Magical flowers!!

A  devotee goes to three temples,  temple1, temple2  and temple3  one after the other. In front of each temple, there ...Read More »
• ### How many times a day do all three hands of analog watch overlaps?

There is a perfectly accurate analog watch with hour, minute, and second hands. How many times a day do all three ...Read More »
• ### Tuesday, Thursday what are other two days staring with T?

Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »
• ### How could only 3 apples left

Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »
• ### How Many Eggs ?

A farmer is taking her eggs to the market in a cart, but she hits a  pothole, which knocks over ...Read More »
• ### Minimum number of persons needed to cross a Desert

In the middle of the confounded desert, there is the lost city of “Ash”. To reach it, you will have ...Read More »
• ### Lateral thinking sequence Puzzle

Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »
• ### Pizza Cost Math Brain Teaser

Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for \$10. It turned out ...Read More »
• ### Which room is safest puzzle

A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »
• ### Overthrow your math teacher!

Some numbers are very mysterious. They are all integers. They have more than one digit. If you multiply them with ...Read More »