Wednesday 20 December 2023

Coincidence and probability

 

Lots of people struggle to understand the way probability works, and the fact that some ‘coincidences’ are relatively easy to predict. The classic example is the birthday problem which shows that in any group of 23 people, there is a 50% probability that 2 of them will share a birthday, and as the number in the group increases, so the probability also increases, until it becomes close to a certainty in a group of around 50. With there being 365 days in a year, it’s a result which just ‘feels’ wrong to most of us.

Other ‘coincidences’ are rather harder to predict. Millions of people update or replace their smart phones every week, and most of the time, it’s a process which is smooth and painless; but for a tiny minority something goes wrong and data is lost. That can also happen even if the phone isn't being replaced, although finger problems rather than technological ones are a likelier cause. I don’t know what the probability of that happening to any one individual is, but it’s going to be a very small number. It would be an amazing coincidence if three people who worked closely together all managed to lose all the data from precisely the same time period, and it's not an outcome which many people well-versed in probability theory would predict. It would be even more astounding if those same messages were then found to have mysteriously disappeared from the phones of those who had received them as well.

Still, being vanishingly unlikely isn’t the same as having a probability of zero, and sometimes highly unlikely events can happen. One doesn’t need to be a conspiracy theorist to wonder, though, whether there might not be a simpler and more probable explanation, perhaps relating to questions such as honesty and truthfulness.

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