I find the way statistics are used in these things really frightening too, and I admit I don't really understand how they work. A quick google says that the odds of winning the UK lottery jackpot are 1 in 14 million. For each individual person, it's almost impossible but it does happen to somebody almost every week.
So many people see statistics in something like this and say "Surely you can't think it's just a coincidence?" and I immediately wonder, well what if it is? What are the chances that it is a coincidence? More or less than 1 in 14 million?
We say 'beyond reasonable doubt' but what statistic would qualify as that? Is 1 in 14 million beyond reasonable doubt? In that case, if the lottery winners are exceptionally lucky, are we just accepting that some people are exceptionally lucky and go to prison?
I remember reading an article about someone who won the lottery twice. I don't remember the details but aren't the odds of that just astronomical? In another life, that could be a person on trial who's been as unlucky as that right?
I get that most trials aren't cut and dry and it's very rare we have a fingerprint and DNA and a gun and a person caught red-handed by a large number of trustworthy people, but where do we draw the line of what statistically is acceptable? 1 in a million? 1 in a billion? How likely does it have to be that we say that's good enough to put someone in prison?
The jury thing worries me for the same reason except that's far more frightening. Twelve jurors really isn't a lot at all, especially when you consider how much the average person can understand complex medical information and especially when you consider social psychology concepts about conformity and certain people having more 'sway' in groups, regardless of whether they actually have more expertise. If you let ten juries (120 people) watch a trial, surely it's unlikely they would all come to the same conclusion. If 9 of them would find you not guilty and 1 find you guilty, for example, then that's still a pretty terrifying roll of the dice to take!
I get that it's the best we have and I don't have an alternative to propose, but I feel like a lot of people see the jury trial as really robust and actually I think surely it's massively up to chance whether they get it 'right' or not. It might be the best thing we have but I would absolutely not want to be on trial as an innocent person and have to trust they'd get it right.