[EM] For series of unrepeatable events

[MIKE OSSIPOFF]

When I tried to post this message earlier, it didn't seem to post,
and so I'm re-posting it, or at least the main part of it:

Most likely this is one definition that we'd find, for the
probability of an unrepeatable event, were we to look it up:

A probability is a number that's a property of a possible outcome
of an event that hasn't happened yet, such that:

If Ei are a series of events, and each has some possible outcome Oi,
such that the number referred to in the previous paragraph is the
same for all of the Oi, then, by examining sufficiently many Ei,
we can make (the number of the Oi that occurs)/(the number of Ei)
as close to that number as we want to make it be. Since that number
is the same for all the Oi, we say that all of the Oi have the same
probability.

If we're talking about one solitary unrepeatable event E1, then
the probability of a particular outcome O1 of that event is defined
as what it would be if a number of other events were added to
that event, to make a series of events, so that each of the newly-added 
events Ei has some
outcome Oi such that that number referred to in the paragraph before
last, and named an outcome's probability, is the same for the Oi
of all the new Ei as it is for the original event's outcome O1.
Now E1 is the 1st event in the series of Ei, and the previous paragraphs 
define the probability of the Oi, one of which is O1.

That's what the probability of 01 means, when Ei is a solitary
unrepeatable event and O1 is a possible outcome of E1.

[end of definition]

This is a natural extension of the usual frequency definition of
probability, for repeatable events, extended to unrepeatable events.

Mike Ossipoff



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