What are the chances?

Randomness is something that most of us struggle to understand - it's one of the main reasons I wrote my book Dice World to explore the influence of randomness and probability on our lives. I try to make randomness something that's better understood by the reader.

However, not everyone has read the book (yet) and confusion caused by randomness often comes up in the media. So, for example, in a recent article on jury service entitled What Are You Chances of Being Called up Again and Again we were regaled with the statement
Plenty of people go through their lives never being summoned; others are called repeatedly. Is selection really, as the government says, entirely random, or is something else at work here?
Now, to be fair to the writer of the article, Patrick Collinson, he does go on to explain that, yes, it is entirely random. But there is definitely a strong implication in that statement that the selection process can't be random if some people get repeated calls and others none.

This is an indirect example of the process known as clustering. We tend to assume that randomness means that the results are well spread out, but actually something that occurs at random tends to crop up in groups, with gaps. When a series of events happen one after the other (clustered in time) or at the same location (clustered in space) we tend to assume that there is a linking cause, that this can't be a totally random occurrence. Historically this effect might have resulted in, say, a cluster of illnesses being blamed on a witch - these days (in many countries, at least) it's more likely to be a phone mast, power lines or a nuclear plant that gets the blame. This doesn't mean, of course, that clusters can't have a cause - however, just because there is a cluster doesn't mean that it has a cause.

So, if selection is truly random, we should expect some people to be called for jury service many times and many never. (Me included, so far.) A useful analogy is to think of taking a tin of ball bearings and dropping them on the floor. You would be really surprised if the balls were all neatly, evenly spread out across the floor. It seems perfectly reasonable that in reality some will be clustered together and there will be gaps with nothing. That's because we don't expect causality here. But in any circumstance with a little more room for causality, such as jury selection, our brains lose their grip on randomness, look for conspiracy and get it very wrong.