This problem is part of our collection Great Expectations: Probability Through Problems.

During 2012, the British government has been considering culling badgers in parts of the UK, because of fears that they help spread TB among cattle.  In October, the proposed cull was delayed until summer 2013.  One reason given for the delay was the unexpectedly high numbers of badgers.

But how do scientists estimate the number of wild animals in a given area?

One way is to use the method of capture-recapture.  Suppose scientists trap and electronically tag a number of badgers on one occasion, then release them back into the wild.  They then set up detectors with cameras in several locations around the forest.  Some time later, the scientists return to collect the cameras.  They look at all the images, recording how many badgers there were, and how many of them were tagged.

In this simulation we're going to use a bag of coloured counters (or multi-link cubes, or similar small objects with different colours).  Choose one colour - this is going to represent the tagged badgers.  The bag represents the area being sampled.
• Count how many counters there are altogether of your chosen colour - this corresponds to tagging badgers on the first occasion.  Record this number.
• Shake the counters up in the bag.
• Scoop out a good handful of counters and count how many of your particular colour there are in your handful, and how many counters there are altogether.  Record both values.  This corresponds to counting how many badgers were in the pictures and how many of them were tagged.
You should now have three figures recorded.
Can you see how to estimate the size of the population from them?

Repeat the experiment a few more times.
What estimates do you get for the total population of counters in the tub?