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Thursday, February 16, 2012

Children in a country

In a country in which people only want boys every family continues to have children until they have a boy. If they have a girl, they have another child. If they have a boy, they stop. What is the proportion of boys to girls in the country?

Ans:
The possibile sequence and the respective probabilty of new born can be:
B - 1/2
GB - 1/2*1/2
GGB - 1/2*1/2*1/2
GGGB - 1/2*1/2*1/2*1/2
...
...
After Summing it up. Total Number of Boys is: 1/2 + 1/2*1/2 + 1/2*1/2*1/2 + ... = 1 On the same lines, Total number of Girls is: 0 + 1/2*1/2 + 2 * 1/2*1/2*1/2 + 3 * 1/2*1/2*1/2 + ... Which also, give 1 on summing up.
Answer is 50/50
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