The problem with probability

International studies of mathematics reveal that the teaching of probability takes up relatively little time within the mathematics timetable. This is simultaneously disappointing and unsurprising.

• Disappointing because probability and the associated understanding of risk should contribute hugely to the development of well-informed citizens. In an era when we are surrounded and bombarded by media articles and public figures offering often dubious statistics, it is important that we prepare the next generation to be able to evaluate these critically and make informed judgements.
• And it’s unsurprising because, historically, probability is a notoriously difficult topic to teach and difficult to learn, and often teachers are reluctant to spend longer on it than is absolutely necessary. Much of students’ experience, therefore, is squeezed into a short period of time in which they skim the surface of probability and simply learn to answer high-stakes assessment questions by rote.

These problems can be compounded when the questions that students and teachers focus on turn probability into an abstract algebraic exercise, without any real connection to everyday experience or students’ understanding of likelihood. Consider the following question from a (nameless) examination board:

Consider three events A, B and C. A and B are independent, B and C are independent and A and C are mutually exclusive. Their probabilities are
p(A) = 0.3, p(B) = 0.4 and p(C) = 0.2.
Calculate the probability of the following events occurring:

1. Both A and C occur.
2. Both B and C occur.
3. At least one of A or B occur.

How does your own experience of teaching probability compare to this picture?