Why do this problem?
Along with X-Dice
, this is a
for thinking about conditional probability.
Simply pose the challenge and encourage experimentation and
calculation to begin with. There is no strictly 'linear' way into
this problem: creativity and tinkering is required to end up with a
valid set of dice. However, all students should eventually find a
Once a set of dice with the correct properties has been
invented and assessed move onto the question of the existence of
a totally fair set of dice. You might begin this by asking who
does or doesn't think that such a set of dice exists, using their
intuitive reasoning. At the end, see who was correct.
How can we determine whether one die is likely to beat
Investigate the variances of your set of dicey dice. Or try
as referred to in the notes and background.
Simply invent pairs of dice and see which is better than the
You can read about some of
the issues which might arise when teaching probability in this article.