[EM] Unrepeatable probability definition wrapup

[MIKE OSSIPOFF]

This is the final wrapup on definitions of probability of
an outcome of an unrepeatable event.

My frequency definition can be better worded, like this:

A probability is a number Pi that's a property of an outcome Oi of
an event Ei.

If there's a series of events Ei, each of which has some possible outcome
Oi, and if we can make
(the number of the Oi that occur)/(the number of Ei that we do) as
close as posible to some number P, by doing a sufficient number of
events Ei, then if the Pi are all equal, then they're are all equal to P.

[end of definition]

In my wager definition of probability for unrepeatable events, I
worded it as I did to show that it was only a sufficient condition.
A better-sounding wording would be:

The probabiliies of the wagered-for outcomes of the Ti are numbers such that 
if all the Ri are greater than 1/Pi - 1, then we can make the
wagerer's gain as large as we want to by doing sufficiently many trials,
and if all the Ri are less than 1/Pi - 1, then we can make the wagerer's
loss as large as we want to by doing sufficiently many Ti.

That sounds more like a definition.

But if we add "if all the Pi are equal", then "numbers" in the paragraph
before last can be replaced by "the numbers", making the definition into
a complete definition.

Mike Ossipoff


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