# Ratio of Boys and Girls in a Country where people want only boys

1,229.4K Views
Answered

In a country,
All families wants a boy. They keep having babies till a boy is born.

What is the expected ratio of boys and girls in the country?

SherlockHolmes Expert Asked on 10th August 2015 in

• 1 Answer(s)
Best answer

Total Probability =ΣProbability of event  = 1/2 +1/4 +1/8 + …= 1

Now,
Expected no of Boys will be
= Σ Probability of event x Number of Boys in that event
=1/2 x1  + 1/4 x1  + 1/8 x 1  +  ….
= 1/2+1/4+1/8+1/16+…
= 1
Expected no of Girls will be
= Σ Probability of event x Number of Girls in that event
=1/2 x0  + 1/4 x1  + 1/8 x 2  + 1/16 x 3  ….         (See tree diagram)
= 1/4+ 2/8 + 3/16+ 4/32 …
=Sn
Sn          =     1/4+ 2/8 + 3/16+ 4/32  +…
1/2x Sn   =            1/8 + 2/16 + 3/32+ 4/64 +…   (Shifting all terms to right)
————————————————————-
Sn/2        =    1/4+ 1/8+ 1/16 + 1/32 +…              (Subtracting)

Sn/2 =  1/4 x 2
Sn = 1/4 x 2 x 2 =1

Expected no of Girls will be =1

Therefore
Ratio of no of Boys to Girls =
Expected no of Boys    = 1   = 1:1
Expected no of Girls       1

Detective Expert Answered on 10th August 2015.
• ### Your Answer

By posting your answer, you agree to the privacy policy and terms of service.
• ## More puzzles to try-

• ### What is the logic behind these ?

3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...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 »
• ### 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 »
• ### (Advanced) Cheryl’s Birthday Puzzle

Paul, Sam and Dean are assigned the task of figuring out two numbers. They get the following information: Both numbers ...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 »
• ### 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 »
• ### Most Analytical GOOGLE INTERVIEW Question Revealed

Let it be simple and as direct as possible. Interviewer : Tell me how much time (in days) and money would ...Read More »
• ### Lateral thinking sequence Puzzle

Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read 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 »
• ### 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 letter replaces the question mark

Which letter replaces the question markRead 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 »
• ### Richie’s Number System

Richie established a very strange number system. According to her claim for different combination of 0 and 2 you will ...Read More »
• ### Srabon wanted to pass

The result of math class test came out. Fariha’s mark was an even number. Srabon got a prime!! Nabila got ...Read More »
• ### Become Normal!!

Robi is a very serious student. On the first day of this year his seriousness for study was 1 hour. ...Read More »
• ### Sakib Knows The Number!

Ragib: I got digits of a 2 digit number Sakib: Is it an odd? Ragib: Yes. Moreover, the sum of ...Read More »
• ### What is the age of grand father puzzle

A boy asks his father, “what is the age of grand father?“. Father replied “He is x years old in ...Read More »
• ### Maths Genious Riddle

If u r genius solve it:- 40 * 14 = 11 30 * 13 = 12 20 * 12 = ...Read More »