Thursday, September 11, 2008

The City Population Puzzle

The City Population Puzzle
A mythical city contains 100,000 married couples but no children.
Each family wishes to “continue the male line”, but they do not wish to over-populate.
So, each family has one baby per annum until the arrival of the first boy.
For example, if (at some future date) a family has five children, then it must be either that they are all girls, and another child is planned, or that there are four girls and one boy, and no more children are planned.
Assume that children are equally likely to be born male or female. Let p be the percentage of children that are male at the end of year y.
How is this percentage expected to evolve through time?
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