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In your recent book , you state that extremely unlikely events are commonplace. How so?
At first glance, it sounds like a contradiction: if something is highly improbable, how can it possibly be commonplace? But as you dig deeper you see it is not a contradiction, and that you should expect what appear to be extremely improbable events to occur quite often. The principle itself is really an interweaving of five fundamental laws.

Could you give an example of one of those laws?
Take the law of truly large numbers. The most obvious example of this is the lottery. In the UK you have a 1 in 14 million chance of winning if you buy just one ticket. But of course if you get enough people buying enough tickets it becomes almost inevitable that somebody somewhere will win. Another example is the chance of being struck by lightning. Around the world there鈥檚 a 1 in 300,000 chance of being killed by lightning in any one year. The rational thing is to behave as if it鈥檚 not going to happen to you. But there are 7 billion people in the world, so there are a lot of opportunities for it to happen. In fact the chance that no one will be killed is about 10鈭�10,133. So we should expect to see someone killed. In fact about 24,000 people every year are killed by lightning, and about 10 times that many are injured.

鈥淎 lot of what look like patterns in data just appear by chance鈥�

People often notice coincidences and patterns that aren鈥檛 really there. Why?
Our ancestors survived in the world because they identified patterns: if you responded to movements in the grass you could avoid being killed by an approaching tiger. So there鈥檚 an evolutionary reason. But a lot of what look like patterns in data just appear by chance.

Such as the 鈥渉ot hand鈥� effect?
The hot hand effect in sport is a good example. This says that if you get a sequence of successes, you鈥檙e more likely to continue in that vein. There鈥檚 a very strong belief in this phenomenon, but the data show it isn鈥檛 really true. It鈥檚 just that people tend to underestimate the frequency with which little bursts of lucky shots occur. It鈥檚 the same phenomenon that leads people to underestimate the frequency with which pairs of consecutive numbers, like 8, 9 or 23, 24, occur in lottery draws. The belief in the hot hand effect changes how players behave. In basketball, teammates will often pass the ball to players believed to be in a hot streak. This gives them more opportunity to score, and if that translates into more points, it can reinforce the impression of a hot streak.

What are the other common mistakes that people make?
A common one is the prosecutor鈥檚 fallacy. In a trial, the jury might be told by the prosecutor that it would be highly improbable for the defendant鈥檚 fingerprints to be at the scene of the crime if he were innocent. Since his fingerprints are there, this is taken as proof that he鈥檚 not innocent. But that鈥檚 wrong. What we really want to know is the probability that he is innocent, given that his fingerprints were at the scene. These two probabilities can be very different. Another mistake is the base rate fallacy, where you focus on a risk that might be serious, disregarding the fact that the chances of it are very small. For example, you might worry about contracting a rare disease, when in the fact that the probability is tiny.

Does the proliferation of choice in today鈥檚 world make us more prone to flaws in thinking?
I think it does. I remember once when my umbrella was broken and it started raining, so I popped into a shop to buy a little collapsible umbrella. I was looking at this rack of umbrellas trying to decide which one I should buy when the shopkeeper called out to me, 鈥淚f you come back tomorrow we鈥檒l have an even bigger choice鈥�. That was the last thing I wanted! The modern world certainly increases anxiety because we鈥檙e aware of the choices.

How seriously do you think our misreading of chance events impacts on our daily lives?
I don鈥檛 think it has a huge impact. After 9/11, people switched from flying to travelling on roads, and because road travel is more dangerous, more people died as a consequence. However, the probability of being killed either way is still pretty small. It鈥檚 true that by driving, people increased the small chance that they would die in an accident, but on average there was a lot less anxiety.

Has your research in this field changed the way you live yourself?
Probably not. People often ask me whether understanding these things takes the mystery away from amazing events. I say, no, it doesn鈥檛. We understand the physics of the rainbow now, but we still look at it and think, wow, isn鈥檛 that wonderful. I鈥檇 go further and say if you understand it, that makes it even more wonderful and exciting.

Read more: 鈥�Chance: How randomness rules our world鈥�