Problem:

In a country where everyone wants a boy, each family continues having babies till they have a boy. 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)


Solution:


So suppose there are N couples. There will be N boys.

1/2 have a boy and stop: 0 girls

1/4 have a girl, then a boy: N/4 girls

1/8 have 2 girls, then a boy: 2*N/8 girls

1/16 have 3 girls, then a boy: 3*N/16 girls

1/32 have 4 girls, then a boy: 4*N/32 girls


So, if we use mathematical formulas the number of girls nearly becomes equal to N.


Since the number of boys is N, the ratio is nearly 1:1.

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