Why do this problem?
provides a framework for discussion about risk and
probability and highlights the stark differences between
experimental and theoretical probability.
You can use this resource at various points in a probability
or statistics course. Because the questions aren't simply of the
'calculate this' form, rich disussion should occur, along with
various probabilistic computations. It will be very useful to
get students thinking about how to formulate questions in
statistics and raise many issues concerning chance, averaging and
You might work through many questions in a single lesson or
split the questions up and use them as short starters to help get
students into statistical frames of mind.
Does the result of a particular flip depend on the results of
an previous flips?
Students can try to invent their own questions based around
this activity. They might also consider trying 'Discussing Risk and
Students might find the open parts confusing in this problem
or they might simply not be ready for the necessary probabilistic
calculations. You could re-formulate the questions in a closed
'calculate this' way. Alternatively you could simply suggest that
students try to clearly explain what needs to be calculated and
discuss how if might be calculated in principle, focussing on which
parts are dependent and which parts independent.
You can read about some of
the issues which might arise when teaching probability in this article.