Use progame to prove math problem

Monty Hall problem

see: https://en.wikipedia.org/wiki/Monty_Hall_problem

Boy And Girl Problem

In a country in which people only want boys every family continues to have children until they have a boy. If they have a girl, they have another child. If they have a boy, they stop. What is the proportion of boys to girls in the country? see: http://mathoverflow.net/questions/17960/google-question-in-a-country-in-which-people-only-want-boys