Monday, April 28, 2014

Surname's on an island

On an isolated island each person has
1/5 probability of having 0 kids
1/5 probability of having 1 kid
1/5 probability of having 2 kids
1/5 probability of having 3 kids
1/5 probability of having 4 kids

Heterosexual partners are chosen at random from the population within the given generational cohort.

It is an old fashioned place where the men pass on their surname to their children,
the women don't.

Initially, the surname Klimpt is not very common. Just 1.00% of the total population.

After 100 generations what is the probability there there will be at least one person called Klimpt in the youngest generation if:
      (i) the initial generational cohort had 400 members
or   (ii) the initial generational cohort had 4,000 members

Express your answer as a percentage with two digits after the decimal point.

Assume that the starting population is half men, half women and that there is a 50-50 chance that each child born is a boy or girl.

Hint: you are probably going to need a computer for this one.

1 comment:

Philip Kinlen said...

The key idea here is that uncommon surnames can become extinct, this is particularly noticeable in small populations. Once the surname has died out, it doesn't recover.