In this resource from the DfE Standards Unit, students discuss and clarify some common misconceptions about probability. This involves discussing the concepts of equally likely events, randomness and sample sizes.
The suggested tasks are based around a set of cards, to which the response might be ‘true’, ‘false’ or ‘unsure’. The commentary explains why the questions have been asked. For example, one card proposes that 1, 2, 3, 4, 5, and 6 are less likely to appear in the lottery than 3, 12, 26, 37, 44 and 45. The commentary argues that people often regard ‘special’ numbers in a different way from ‘ordinary’ numbers, when considering their probability.
In the research literature, Kahneman and Tversky’s heuristics on people’s judgements of chance offer one account of this phenomenon.
The aim is to reveal some common misconceptions. It is not clear that revealing such issues is sufficient, and students may not believe the explanations as to why some responses are wrong. Nevertheless, the tasks might provide some useful groundwork that can be followed up in other ways.