Understanding stats is vitally important – whether it comes to working out your pension, understanding screening programmes for disease or placing a bet on the winner of the Tour de France. But stats isn’t always easy. Measures of risk, for example, can be ‘tricky stuff’, says David Spiegelhalter, the eminent Cambridge statistician.

That’s why a new study commissioned by the Nuffield Foundation is welcome. It looks at how children grasp probability, and ways in which this basic statistical concept might be taught in primary schools. According to Professor Peter Bryant and his colleagues a good starting point is children’s intuitive responses to ideas of fairness. What better way to begin a card game than to shuffle the pack – by randomizing the distribution of cards you make the game fair.

The study says ‘despite the central importance of randomness and probability in our lives, it is clear that children (and many adults as well) often have great difficulty in thinking rationally about, and quantifying, probability’.

To get there we need to understand randomness, to work out the ‘sample space’ (all the possible events that could happen), understanding how events might be related (correlation) and then probabilities to be given a numerical value.

Psychologists show that people tend to think of ‘natural sequences’. If you pick four purple balls out of a bag containing only yellow and purple balls, there’s an almost intuitive belief that ‘it’s more likely’ the next ball to come out will be purple. But some people think ’the chances are’ the next ball has to be yellow. Teaching probability elicits the right answer: the chances of the next ball being either yellow or purple are the same.

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