Yes. Your chance of being hit by lightning in a given year is quite low. The average number of people struck by lightning in the US annually in the last decade is 270, according to https://www.weather.gov/safety/lightning-odds (and while that's an estimate, the 27 average deaths/year over that period is not).
So a specific person being killed by lightning within a given year is pretty unlikely (less than one in 10 million chance), and on average it happens once every two weeks in the US. Lots of people, see.
Same thing with other situations where there are lots of observations...
Any given unlikely event does not happen very often.
But if you have a whole bunch of possible unlikely events, then one of them (a different one each time, usually) can happen fairly often.
Back to the lightning example, any given person being hit by lightning is an unlikely event. But as you not "someone being hit by lightning" is not, because we are now observing these unlikely events across so many people.
All of which is to say, observing that an unlikely event happened doesn't provide much information on its own, if you have observed a lot of things happening in general...
Beautifully put - I nominate this as the official summary of the subthread. It's the reason why we need to pad time estimates for projects and leave early to catch trains, even when we can't think of any likely reason for delay - the sum of all unlikely reasons can cross the threshold into "likely".
So it's quite correct to say "unlikely events happen all the time".
The odds of you dying from any particular unlikely death (like lightning) is super low. The odds of you dying of any of them (bear mauling, tied to a railway track, spontaneous combustion, etc) is significantly higher. That's the sort of thing I mean.
Individual coincidences are rare. But if you start really looking for them, you will absolutely find some coincidence. The one that happens will have been unlikely and impossible to predict ahead of time, and yet you were more or less absolutely certain some coincidence would occur, because there are so many possible configurations of coincidence that one is bound to happen.
So a specific person being killed by lightning within a given year is pretty unlikely (less than one in 10 million chance), and on average it happens once every two weeks in the US. Lots of people, see.
Same thing with other situations where there are lots of observations...