I was doing a trial the other day when the first 9 jurors chosen from the jury in waiting were women. The prosecutor and myself exchanged an arched-eyebrow look, as it seemed a possibility that we might get an all female jury. We didn’t. Although we did end up with 10 women and 2 men, which does feel a bit ‘unbalanced’.
Talking about this afterwards, I saw an all female (or all male for that matter) jury as a bit of a curiosity. It was something that would happen, but it would just be unlikely to happen to me. However, I was surprised at how many people thought that this was a bit sinister, and potentially a sign that the jury was rigged. Or, at the very least, some shenanigans had gone on in the list office to mean that the process was not random.
The jury panel was actually mixed, but had more women than men in, but leaving that aspect aside – if jury’s are supposed to be randomly selected, shouldn’t a Judge intervene if there is an female jury?
Doing the maths
There are about 17,000 jury trials a year (17,706 in 2012 but the latest figures for January-March 2015 here indicate a decrease, so this seems a reasonable estimate). There are actually more women than men in the country as a whole – 50.9% of the adult population are women – but this won’t make a huge difference to the calculation, so I’ll assume it’s 50-50
If juries are chosen at random, what are the chances that we will have an all female jury? It’s (1/2)12 = 1/4096 = 0.02%. Unlikely, but not that unlikely. On the basis that there are 17,000 juries sworn a year, it would be surprising if this didn’t happen.
It’s basically the same as getting ‘heads’ twelve times in a row when you toss a coin. Yes, it is very unlikely, but if you toss a coin 12 times on 17,000 occasions however, then it ‘feels’ pretty likely that you’ll get 12 heads at some point during it.
If you want to be a bit more technical, then it’s probably going to be a poisson distribution with λ=4.15 (0.02*17000). This means that the probability of there being no all female juries in a year is low – about 1.6% (which will be the same as the probability of having no all male juries). In other words, even though having an all female jury is very unlikely, the chances of there being at least one all female jury in a year is very high – 98.4%.
This is the difference between something being unlikely to happen at all, and something being unlikely to happen to you. As an example, winning the jackpot on the National Lottery is very, very unlikely, yet most week one or more people win.
It is more than just a little mathematical curiosity however. It’s a symptom of a wider problem in society, and that is a difficulty in understanding probability (have a start listening here if you haven’t already). It can not only damage your health, but can cause a miscarriage of justice as well (see the Sally Clark case as one example, and the less well known case of Wilson  EWCA Crim 1754 as another I’ve looked at previously).
The way I’ve always tried to explain it to juries is with a lottery analogy – the odds on winning the lottery are 14 million (or so) to 1. But if someone says that they have won the lottery, you wouldn’t disbelieve them solely because it is so unlikely. Whether it’s winning the lottery or having an all female jury, when you look over many different occurrences, rare events can become quite common.