**Tough Probability Interview Question - 20 November**

There is a country where everyone wants a boy. Every family continue to have babies till a boy is born. If the probability of having a girl or a boy is the same, what is the proportion of boys to girls after some time in that country ?

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ReplyDeleteShould be about 2.88 girls for every 1 guy.

ReplyDeleteits china

ReplyDeleteLet me see if i've gotten this correct.

ReplyDeleteLet's view it as a series, with an example starting number of 16 couples.

In the first series, 8 couples will have a girl and 8 couples will have a boy.

Those who had a girl the first time will try again, and in the second series, 4 will have a boy and the other 4 will continue to have girls.

In series three, there will be 2 boys and 2 girls.

At the fourth series, there will be 1 boy and 1 girl.

This last couple remeaining will try to have another child. If we continue to go on the idea that out of two of their children, there is an equal chance of having either gender, then they will have either a boy, or a girl and then a boy.

This logic can be used on any scale, until the country's child populace is either 1:1 or the same but with one extra boy.

Every time they try to have a child–no matter what the reason is–chances are 50% for either sex. So the boy-girl ration will always be 1:1.

ReplyDeleteTks very much for your post.

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