Important decisions require an understanding of risk – and, therefore, probability. One might suspect that our political and business leaders might not know much about this or any other branch of mathematics. But, not to worry, we might think – they’ll be advised by people who do.

However, as Nassim Nicholas Taleb has long-argued, the truth is that even the cleverest people can get probability badly wrong.

There’s a brilliant example of this in an article for Priceonomics. It concerns the infamous Monty Hall Problem:

“Imagine that you’re on a television game show and the host presents you with three closed doors. Behind one of them, sits a sparkling, brand-new Lincoln Continental; behind the other two, are smelly old goats. The host implores you to pick a door, and you select door #1. Then, the host, who is well-aware of what’s going on behind the scenes, opens door #3, revealing one of the goats.

“‘Now,’ he says, turning toward you, ‘do you want to keep door #1, or do you want to switch to door #2?’”

The question is whether switching improves the odds of you getting the car. Most people instinctively reject the notion. As it’s a choice of two doors, they assume the chances must be fifty-fifty – i.e. switching makes no difference.

Except that it does. You are twice as likely to get the car if you switch than if you stick with your original choice. If you don’t believe me, then read the whole article which explains the reasoning behind this counter-intuitive conclusion. (My own tip is to think about the odds of both the initially rejected doors having goats behind them – because that’s the only situation in which you lose if you decide to switch).

When the American columnist Marilyn vos Savant discussed the Monty Hall Problem in an article for Parade magazine (not to be confused with the British publication of the same name), the public response was overwhelming:

“…though her answer was correct, she received over 10,000 letters, many from noted scholars and Ph.Ds, informing her that she was a hare-brained idiot.”

Far from being hare-brained, vos Savant has one of the highest IQs ever recorded. Needless to say, some of her critics were more concerned with her X chromosomes than her IQ points:

“The outcry was so tremendous that vos Savant was forced to devote three subsequent columns to explaining why her logic was correct. Even in the wake of her well-stated, clear responses, she continued to be berated. ‘I still think you’re wrong,’ wrote one man, nearly a year later. ‘There is such a thing as female logic.’”

As well as providing a demonstration of sexism in action, the affair was proof that even maths professors have trouble wrapping their heads around the fundamentals of probability.

The relevance to public policy is that we should be sceptical of any claim that experts have fathomed the risks of a particular course of action. For instance, the risk models that played such a disastrous role in the financial crisis of 2008 were created by highly qualified mathematicians.

In his best-selling book, The Black Swan, Taleb explains the fatal flaws in these models – in particular, their inability to account for the impact of rare, but extreme, events. Today, Taleb argues that related conceptual errors are being made in regard to climate change and GM crops, where the risks are much more troubling than conventionally recognised.

Of course, this isn’t an easy argument for most of us to get into. But the next time a politician or expert reassures you about risk, test them on the Monty Hall Problem.