Why do this problem?
This is a very open-ended task in which the learner is encouraged
to contemplate the notion of randomness. Of course, although every
individual pattern has just as much chance of emerging as any other
individual pattern, there are many patterns which are qualitatively
'similar' to each other. Attempting to quantify this 'similarity'
is a good exercise in mathematical thinking.
In discussion, ideas will emerge about the nature of randomness. Be
sure to note that students are all aware that all patterns are
equally likely. It can be used productively at any point during the
study of statistics.
- What can we see?
- What similarities and what differences occur?
- Do any patterns look to the eye less likely than others?
Various further calculations concerning the squares can be
suggested. In particular, how might one estimate the probability
that an individual square is red given a fully coloured grid? How
might we devise a confidence interval for this estimate?
Try the Can't
find a coin?