In a country where everyone wants a kid with a specific gender (assuming only 2
genders), each family continues having babies till they have a kid with the
expected gender. After some time, what is the proportion of boys to girls in the
country? (Assuming probability of having a boy or a girl is the same)
Round off your answer to 2 decimal places and output the answer as
1.xx where I is the integer part of your answer, and xx are the first 2
decimal places of the rounded off answer.
Answers
Given : In a country where everyone wants a kid with a specific gender (assuming only 2 genders), each family continues having babies till they have a kid with the expected gender
To Find : After some time, what is the proportion of boys to girls in the
country?
Solution:
Probability of each gender = 1/2
Specific gender can be as 1st baby or nth baby
Probability Specific Gender Other Gender
1st 1/2 1 0
2nd 1/4 1 1
3rd 1/8 1 2
4th 1/16 1 3
nth (1/2)ⁿ 1 n-1
Specific gender = (1/2) + (1/4) + ................................+ (1/2)ⁿ
= (1/2) (1 -(1/2)ⁿ) /(1 - 1/2)
= 1 -(1/2)ⁿ
other gender
= (1/2)0 + (1/2)².1 + (1/2)³.2 +.................................(1/2)ⁿ (n-1)
= (1/2)².1 + (1/2)³.2 +.................................(1/2)ⁿ (n-1)
∑(n-1)/2ⁿ
Considering n as larger number
1 -(1/2)ⁿ = 1
∑(n-1)/2ⁿ = 1
Ratio would be 1 : 1
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Answer:
In a country where everyone wants a kid with a specific gender (assuming only 2
genders), each family continues having babies till they have a kid with the
expected gender. After some time, what is the proportion of boys to girls in the
country? (Assuming probability of having a boy or a girl is the same)
Round off your answer to 2 decimal places and output the answer as
1.xx where I is the integer part of your answer, and xx are the first 2
decimal places of the rounded off answer.