A strange country
In a country, all families want a boy. They keep having babies until a boy is born. If the expected ratio of boys to girls in the country is , where and are coprime positive integers. What is ?
The answer is 2.
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1 solution
The chance of having a boy is 1/2. Therefore, the expected number of trials before having a boy is 1/1/2 = 2. Therefore, each family is expected to have 2 children. The first is a girl hence, they have another one who is a boy. The ratio is therefore 1:1. 1+1 = 2.