The genders of the neighboring family’s children
The house next door has some new neighbors. They have two children, but you don’t know what mix of boys and girls they are. One day, your wife tells you “At least one of the children is a girl”. What is the probability that both are girls?
Your wife then tells you “The way I found out that at least one of the children is a girl is that I saw one of the children playing outside, and it was a girl”. Now, what is the probability that both are girls?
There are four possibilities for your neighbor’s children: BB, BG, GB, and GG. All of these are equally likely.
Once your wife tells you she knows one of the children is a girl, you have eliminated the possibility that the children are BB. There are three possibilities left, and the remaining possibilities are still all still equally likely, so there is a 1/3 probability that both children are children.
However, when your wife says “The way I found out that at least one of the children is a girl is that I saw one of the children playing outside, and it was a girl”, the probability changes. Using Bayes’ rule,
P(GG | child wife saw was G)
= {P(GG)P(child wife saw was G|GG)} / {P(child wife saw was G)}
= {P(GG)P(child wife saw was G|GG)} / {(P(BB)P(child wife saw was G | BB)) + (P(BG)P(child wife saw was G | BG)) + (P(GB)P(child wife saw was G | GB)) + (P(GG)P(child wife saw was G | GG))}
= {(1/4)(1)} / {(0(1/4)) + ((1/2)(1/4)) + ((1/2)(1/4)) + (1(1/4))}
={1/4} / {1/2} = (1/4) * (2/1) = 2/4 = 1/2.
So after the second bit of information, the probability the second child is a girl is 1/2, which matches our intuition
Your Answer
More puzzles to try-
Strange in Sea
Who is the strange one who lives in the sea, he has eight arms but no legs ?Read More »Orange Distribution riddle
A kind gentleman decided to give 10 oranges to each of the girls in his town and 5 oranges to ...Read More »12345 is an Actor
12345 a famous South Indian actor 567 is a path in jumbled form 8 & 10 are same letters 9 ...Read More »Dark with White
Dark with white markings, And smooth like a rock. Where learning occurs, It helps convey thought. What is it?Read More »Fish without an eye riddle
What do you call a fish without an eye?Read More »The Gravity on Mars
Two Martians and two Earthlings traveling together came to a canal. As a result of the gravity on Mars, the ...Read More »Long Night
A Boy had just got out of the shower and getting ready for his prom,shaved,and with cologne and there was ...Read More »Find the missing Number
Find out the missing number in the picture attached:Read More »No voice yet I speak to you riddle
I have no voice yet I speak to you, I tell of all things in the world that people do. ...Read More »NDA Exam-I 2011 – Which letter replaces the question mark in circle?
Which letter replaces the question mark in circle?Read More »A MAN IN AN ELEVATOR
A man who lives on the tenth floor takes the elevator down to the first floor every morning and goes ...Read More »What is his age
When Jacob is twice as old as John, Then I shall be just 17. But Jaco was 23 When John ...Read More »Peacock and egg puzzle
If a peacock and a half, lay an egg and a half, in a day and a half. How many ...Read More »Position in the Car Race Puzzle
Okay before we begin with the puzzle, remember that you have to answer it quickly. You are participating in a ...Read More »Divide barrels and wine evenly
A man is the owner of a winery who recently passed away. In his will, he left 21 barrels (seven ...Read More »What get longer when you pull it?
What gets longer when pulled,fits between breasts, slides neatly into a hole,has choked people when used improperly,and works best when ...Read More »A,B,C ology puzzle
Astrology starts with the alphabet A. Biology starts with the alphabet B. Limnology starts with the alphabet L. Can you ...Read More »What is it?
No matter how much rain comes down on it it won’t get any wetter. What is it?Read More »Full Name Guessing Riddle
???? Do you know the full form of these words❓❓ ?? NEWS PAPER – ?? CHESS ?? COLD ?? JOKE ...Read More »Traveller trapped by king puzzle
A very intelligent and kind Traveller was trapped by a King, King wants to check his intelligence and kindness at ...Read More »