I was discussing this event with my daughter this morning, and it ended up being an instructive discussion on random events of very low probability. If we are totally oblivious of the satellite orbit, and forget different likelihood of earth surface points for the re-entry (the very north and south latitude are much less likely), we can try and compute how likely it is that one of, say, 50 large fragments of the satellite will end up falling within a 100 m^2 area around us -which would be frightening enough.
The earth has a surface of 500 million square kilometers, and a square km contains a million square meters; so that makes it a one-in-five-trillion chance per each fragment, or one in hundred billion chance that one fragment gets that close to us. Upon hearing that big number, my 10-year-old daughter got more worried than I expected. So I had to put this number in perspective.
I think I found a good way to reassure her, by comparing that probability to that of another very rare phenomenon which does not appear to happen at all anyway. I took a powerful earthquake in our area as the comparison stone. Venice, the place where we live, has not witnessed such an event for at least a thousand years; so, since in a thousand years there are three trillion seconds, one may say that the chance of a powerful earthquake hitting us in the next thirty seconds was similar to the chance of one satellite fragment on our path.
Ilaria started to count to thirty, and soon agreed that yes, that did look quite unlikely after all. I could then end the discussion by explaining that what we consider random events sometimes are not random at all, but perfectly well-determined; it is just our ignorance which prevents us from calculating with precision that an event will occur with probability one, or zero.
I guess I could have continued by explaining that from a frequentist point of view, when we say that our error bars on some measurement have a likelihood of covering the true value of the measured parameter with 68.3% probability we are just expressing our ignorance on the true location of the parameter, and we need to bear in mind that the probability is actually always either zero or one: the interval is a member of a set of possible intervals we had a chance to draw, whose coverage properties are owned by the set and not by any one of the individual elements - the possible error bars. The random variables, in such an example, are the extrema of the interval !
... But I think this would have been too much for a ten-year-old girl.
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