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 ?
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.
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.
In order for the information about which dime was heads to be useful, you have to make an assumption regarding the complete information available to me and *why* I selected to share order information about the dime and not the penny, as well as *why* selected to share information about shininess about the penny. If I know the result for both dimes, then the information about which was flipped first is useless: I would not revel information about a coin being tails, so I would always select to tell about the dime that came up heads. Same logic applies to the pennies. Since the selection bias is to only tell about heads, the information about order or shininess is irrelevant because it is revealed AFTER the selection of which dime to reveal is made. Information about order, shininess, etc. is only useful if it is ARBITRARILY revealed.
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.
Your Answer
More puzzles to try-
Find the Errors
Can you find the 09 errors in the picture below?Read More »Mall Store Puzzle
John Went to the nearby store in a Mall to buy something for her home. Below is the conversation between ...Read More »Why not?
A man has hundreds of bodies buried on his land, many of which are cops and criminals. Many people find ...Read More »1 to 9 all digits to be used puzzle
Use digits from 1 to 9 once in such a way that each digit is used in the boxes and ...Read More »Truth or Liar
John and Jacob are twin brothers. One of them is a liar whereas the other one is a truth-teller. I ...Read More »Always Ahead
It is always ahead of me yet I can never see it. What is it?Read More »5 Little creatures riddle
We are very little creatures. All of us have different features. One of us in glass is set; one of ...Read More »Relationship Numbers Riddle
Replace the question mark with the correct number to complete the series, given the pair of numbers exhibits a similar ...Read More »You can’t find out!!!
Fariha, Ononno, Richie each got a prime. Suppose the numbers are A,B,C. They permute the numbers in the following possible ...Read More »I am under you
I am under you when I am whole. I shift above you if you remove the first letter. I come ...Read More »Mother’s Brother
Your mother’s brother’s only brother-in-law is asleep on your couch. Who is asleep on your couch?Read More »Baby falls out
How could a baby fall out of a twenty-story building onto the ground and live?Read More »Rounding Off Numbers
Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get ...Read More »Time puzzle
Supposing a clock takes 7 seconds to strike 7, how long does it take for the same clock to strike ...Read More »Magic Maths
In a Certain Country 1/2 of 5 = 3. If the same proportion holds, what is the value of 1/3 ...Read More »John and Jill Love Riddle
John and Jill are madly in love with each other. To remind Jill of his pure love, John wants to ...Read More »What happened?
A man is found dead in a phone booth in a pool of blood. The glass on either end of ...Read More »Sixth kid’s name
A mother gave birth to six kids. The first daughter’s name is January. The second daughter’s name is February. The ...Read More »Travel but stays in home
I like to roam but I’ll always stay home, He likes to travel but stays in home, He leaves a ...Read More »Three feet but can’t walk
I have three feet, but can’t walk; I tell you things, but can’t talk; Sometimes I bend but, I am ...Read More »