The arithmetic of risk

Abstract

In John Lanchester's novel Mr Phillips , the hero, a newly redundant accountant, is taken hostage during a bank robbery. Lying face down on the ground, he passes the time rehearsing a conversation he'd had with his former colleagues about the statistics of the National Lottery. The chance of winning is about 1 in 14 million, which is much lower than the risk of dying before the week's lottery is drawn. The accountants wondered how close to the draw you would need to buy a ticket for the chance of winning to be greater than the risk of dying. The answer is about three and a half minutes. The calculation is straightforward. Of the 50 million people in England, about half a million die each year, which is about 10 000 a week. The probability of dying during a typical week is therefore about 1:5000, or 3000 times higher than the 1:14 000 000 chance of winning that week's lottery. The probability of dying and the probability of winning are therefore the same when the ticket is bought 1/3000 of a week before the draw, which is about three and a half minutes. A more sophisticated calculation takes age into account, in which case a 75‐year‐old needs to buy a ticket 24 seconds before the lottery is drawn, but a 16‐year‐old could risk buying one 1 hour 10 minutes before. It is an amusing calculation, but as an approach it makes many people uncomfortable, not least because their own death or that of a friend or relative seems not to be properly accounted for by a probability: an individual, after all, is either alive or dead. But as the undertaker and poet Thomas Lynch has said, although individually each body is either in motion or at rest, en masse the picture is very different: ‘Copulation, population, …