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# Sussex mathematician pens a probable winner

20 April 2012

**Sussex mathematician pens a probable winner**

**A University of Sussex statistician’s latest book is likely to be a hit – especially among those keen to understand more about risk and chance.**

John Haigh, an Emeritus Reader in Mathematics, has joined the illustrious list of academics and experts to have contributed to Oxford University Press’s best-selling series of texts, A Very Short Introduction, by authoring one on Probability.

In nine concise chapters Haigh explores ideas of probability and different philosophical approaches to it, as well as giving tips on how to make good decisions under conditions of uncertainty.

For example, he suggests that the concept of “utility” - how useful certain outcomes would be - is a major factor in decision-making. If someone offers to give you £1, or the chance to win £10 depending on the toss of a coin, you might choose to gamble the £10 as winning this would be far more rewarding than the certainty of receiving £1. If you turned these figures into £1,000,000 and £10,000,000, you are more likely to opt for the certainty of the smaller figure. Haigh writes: “For small sums of money, having ten times as much usually

*is*worth tens times as much. But if one million pounds would generate a certain amount of pleasure for you and your family, ten times that amount would not lead to double the pleasure.”

Using easy-to-follow language, Haigh explains the laws of probability and discusses the range of applications of probability theory in science, sport, economics and legal matters.

He also examines how we should interpret headlines that scream about the risk of certain foods or lifestyles on our health. An article may accurately report a study that shows that that eliminating a particular food from your diet “cuts the chances of developing a disease by 50 per cent”. This is the “relative risk”. But the “absolute risk”, based on the sample size, might be that rather than one in a million developing the disease, the abstinence reduces that to one in two million. In other words, the absolute risk might be so minuscule as to amount to zero.

Ultimately, he reminds the reader that: “…the rational action is the one that maximises the mean utility of the consequences. You can never be sure that you have taken the action that would have worked out best, but you have made optimal use of the information you have. You cannot ask for more.”

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