Additional Thoughts

Although mathematically satisfying, the answers we arrived at in our first look are hardly perfect. They leave a number of questions including --

• What happens if each female does not have an infinite number of potential pregnancies?

• Although each generation has the same number of children in the two countries, the average age of the mother childbirth may be different and thus the rate of population growth per unit of time may be different.

• The nature of modeling -- in which we start with a simple model and build progressively more realistic and useful models.

• The fact that intuition often leads us astray in situations involving probability. Did you (would your students) expect the results we obtained? Would your expectations have been different if the same mathematical problem was situated in gambling. A large number of gamblers either bets one dollar twice at even odds or each one continues betting until he or she wins for the first time.