???
...
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 overpopulate. 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(t) be the percentage of children that are male at the end of year t. How is this percentage expected to evolve through time?"
- Note: we are looking at the expected value
- Also notice: it can be explained by Recursion.
- Every year, regardless of the number of newborn children, there will always be equal amount of expected female newborn children and male newborn children.
- Thus, the answer is 50%.
*** It is the first question that made me feel I don't fully understand
what an expected value means. Also, this question made me want to play poker the first time. ***
