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An Ancient Law

“20th June 2015, Crankshire. A lonely and desolate place”, you write in your diary. The mere thought of staying another day in this town is depressing. However, you remind yourself that you are here for a reason. The news editor and chief has sent you to this town personally to help uncover the effect of a long ago passed law on its citizens.

You open the Crankshire Book of Laws to the said ‘Family Law’. You still get the a sense of disbelief as you start reading the passage again.

“We, the People of Crankshire, hereby vow to uphold the Law of Family which was bestowed upon us in the year 1790.  We commit to bearing children until the birth of a son.”

At the time, there was a belief that a society made up of more women would result in a more peace-loving society. And so the law was passed, that families shall continue bearing children until they have a son. After which they will stop procreating. The genealogy of the town confirmed that this law was indeed upheld.

What effect did this law have on the proportion of males vs females?

Answer
The law does not have an effect on the proportion of males vs females, since the chance of having a boy or girl is independent of what happened previously. Stated differently, assuming there is a 50/50 chance of having a boy or a girl, if 100 women have the children, the odds are there will be 50 boys and 50 girls. Therefore according to the law, only half that had girls will continue to bear children. Out of that number they will again have an equal number (proportion) of girls and boys. In the third round of procreation, the same odds will be repeated until the population is in the same proportion as before.
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Stating the obvious here, but I enjoy riddles & puzzles. Anyone else also struggling with seemingly simple 5th grade math problems?

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