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> 100% means the event is certain to occur

Actually, 100% means the event is "almost certain". That's not an accidental choice of words; it's a technical term which conveys important meaning about how we reason about probability.




That's a distinction without meaning when talking about a finite number of outcomes.


I had to look this up, so for the benefit of anyone else curious:

https://en.wikipedia.org/wiki/Almost_surely

TL;DR: Infinities being weird as usual.


Good read. From that page, here's an example that nicely illustrates the concept:

Imagine throwing a dart at a unit square (i.e. a square with area 1) so that the dart always hits exactly one point of the square, and so that each point in the square is equally likely to be hit.

Now, notice that since the square has area 1, the probability that the dart will hit any particular subregion of the square equals the area of that subregion. For example, the probability that the dart will hit the right half of the square is 0.5, since the right half has area 0.5.

Next, consider the event that "the dart hits a diagonal of the unit square exactly". Since the areas of the diagonals of the square are zero, the probability that the dart lands exactly on a diagonal is zero. So, the dart will almost never land on a diagonal (i.e. it will almost surely not land on a diagonal). Nonetheless the set of points on the diagonals is not empty and a point on a diagonal is no less possible than any other point: the diagonal does contain valid outcomes of the experiment.


Interesting. Of course to do the experiment as described you would have to determine the point the dart hit with infinite precision. If there is any limit to the precision with which you can determine the point of impact, then the probability that the dart hits close enough to the diagonal that you can't tell if it was hit or not becomes finite.




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