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Probability is one of those things we all get wrong… deeply wrong. The good news is we’re not the only ones, says , a mathematician at the University of Sussex in Brighton, UK, and author of . “Many pure mathematicians claim that probability has many unreasonable answers.”
Take the classic problem of a class of 25 schoolchildren. How likely is it that two of them share the same birthday? The common-sense answer is that it is not implausible, but quite unlikely. Wrong: it’s actually just under 57 per cent.
Or the celebrated Monty Hall problem, named after the former host of US television game show Let’s Make a Deal. You’re playing a game in which there are three doors, one hiding a car, two of them goats (see illustration). You choose one door; the host of the game then opens another, revealing a goat. Assuming you’d rather win a car than a goat, should you stick with your choice or swap?
The naive answer is it doesn’t matter: you now have a 50-50 chance of striking lucky with your original door. Wrong again.
But if probability makes even experts grumble, how do we get it right? Simple, says mathematician Ian Stewart of the University of Warwick in the UK: do things the hard way. “The important thing with probability is not to intuit it,” he says. Think carefully about how the problem is posed and do your sums diligently, and you’ll arrive at the right answer – eventually.
With the birthday problem, the starting point is to realise that you’re not interested in…
