If it looks random, it probably isn’t:
This same conditional-probability argument, though, also applies to the day after tomorrow.
There’s a 0.0001 chance of lightning tomorrow. But for the next strike to be the day after tomorrow then lightning must strike on that day, and not strike tomorrow. So the probability becomes 0.9999 for no strike tomorrow, times 0.0001 for a strike the next day. Which is 0.00009999.
This is only very slightly less than 0.0001, but it is less. The probability of the next strike – not any strike, but the next strike – occurring the day after tomorrow is thus very slightly lower than the probability of the next strike being tomorrow.
And the further you go into the future, the smaller the number gets. In a week it’s about 0.00009994, in a year it’s about 0.00009643, in ten years it’s down to about 0.00006943 – until it becomes ridiculously small, millions of years in the future.
So the most likely day for the next lightning strike – whether or not it actually even struck today – is tomorrow. It’s only a tiny bit more likely that the next strike will be tomorrow than that it will be the next day, but it is more likely.
At this point you may be wondering why I’m injuring your brain with this stuff. It’s because this is a really important thing you need to know about the world. This statistical bias for chance events to happen closer to each other than seems intuitively likely means that all sorts of chance phenomena have “clusters” that people naturally think don’t look very random at all.
We are surrounded at all times by things that have a somewhat random distribution in space and/or time. Computer hardware failures. Car crashes. Disease outbreaks. The distribution of stars in the sky. Individual kills, and personal and team victories, in all sorts of games, sports and real-world wars.
None of these things are entirely random – actually achieving true, robust randomness is surprisingly difficult. But all of them have a chance component. And the stronger that chance component is, the more clusters you’ll see, and the easier it’ll be to incorrectly attribute those clusters to some non-chance phenomenon.
[Complicated world form that perspective.]