an interesting use of ratios is in the 'capture-recapture' method for estimating a population size
pull out a sample
mark it in some way
put the sample back
pull out another sample and use the fraction/ratio of marked things to estimate the full population size
suppose 40 butterflies are marked in some way and released in a particular location
then a further 20 are captured as shown:
how many butterflies would you estimate there to be from this information?
this program enables repeated capturing
repeatedly making second captures enables a comparison of different estimates, exploring the variation:
what are the extremes and what is the mean?