Bud Terfli owns 10 acres of property. He's amazed at all the butterflies he sees. He wonders...

How many are there? I'd like to know, but I can't possibly count them all.

Bud consults a statistician, who tells him about a method that produces an estimate of the population size. The method is called Capture-Tag-Recapture.

Bud captures 150 butterflies. He's selected them using a method called random sampling. That is, each possible collection of 150 butterflies was equally likely to have been the captured collection of 150 butterflies.
Bud tags--or marks--each of the 150 butterflies. Each now has a harmless white spot on its left wing. Bud releases the butterflies.
A few days later (the previously captured butterflies have had ample time to distribute themselves about the property) Bud again collects butterflies--this time he collects a random sample of 200 butterflies. Some of them have white spots, some don't. In fact, exactly 17 of them have a white spot on the left wing.

The statistician provides an on-the-spot estimate of the total number of butterflies on Bud's property. Can you?

  1. What number does the statistician report to Bud? Describe the reasoning you use to arrive at this value.
  2. Is this number correct? That is, is this number exactly equal to the true number of butterflies on Bud's property?
  3. What practical difficulties arise when using this method?