Night flying in the mountians in a cessna 150,

"Ron Garret" wrote in message
...
In article ,
wrote:

I think the implication, with all due respect, in the way you worded
your post, is that the probability is increasing as you flying time is
increasing.

It depends on what you mean by "the probability". There
are two different probabilities being discussed: there is the
probability of a failure on any particular flight, which doesn't
change, and there is the cumulative probability of experiencing
failure on some flight, which does change (it increases with
each flight). This is clearly not the case, as I think we all
now agree.

There is also the probability (that Peter (I think) proposed)
stated as a cumulative probability in terms of an arbitrary
large number of trials (flights, or hours, or whatever).

If you convert this to a probability of occcurence with
a lower number of trials (flights, or hours, or whatever)
that probability will be lower. Looked at it this way,
if the probability of an 'occurrence sometime in (the
remainder of )one's career is known, then as the career
progresses, the probability of 'an occurrence sometime
(in the remainder of) one's career diminishes from
that value.

This is a direct consequence of

1) the premises (accepted by all here,
apparently) that

- the probability for any given trial (hour, flight, or
whatever) is assumed to be independent of any other
given trial (hour, flight or whatever) and
- the probability is assumed to be the same for each
such trial, and

2) the assertion that the probability of an occurrence
over n trials is (1-(1-p)^n, where p is the probability
of occurence in a single such trial.

Its the same problem worked back to front (or
front to back, depending on your point of view):

i.e.: Let p2 be the probability of an occurence in
n2 trials, and let p1 be the probability of an occurence
in n1 trials, if n1 n2, then p1 p2.

If you *start* with p1, as you consider an increased number
of trials the probability will increase, if you *start* with p2
and consider a decreased number of trials, the probability
will decrease.

Your statement is ambiguous because you don't say
which probability you're referring to.

Yes. The logical conclusion is determined from
the premises used. You only get out of it what you
put in.

Every day is a new day, and N gets reset to zero.

Not quite. Every day is indeed a new day, but with
every flight N is incremented by one.

It depends on upon from which premise you started.
If you're considering your probability in terms of
occurences per N trials, you might change N if you
start out with it being 'the number of trials in my
entire career', but the probability of an occurence
'in the next N trials' otherwise doesn't need any
change in N from day to day.

But 'the number of trials in my career' is moot
in the first place, and I'd argue that arbitrarily
specifiying the number of trials that are 'going to
occur' in your career is equally problematic, as
is coming up with such a probability in the first
place. The best you can get out this argument, I
think, starting out with a guess for the cumulative
probability of the 'entire carreer', is a qualitative
'probability is decreasing' as the career progresses,
and you can't really ever quantitatively say how
much.

In article P68Ud.515993$8l.368458@pd7tw1no,
"Ron McKinnon" wrote:

as the career
progresses, the probability of 'an occurrence sometime
(in the remainder of) one's career diminishes from
that value.

Yes, but only because N is lower. Whatever N is, after every flight N
is 1 less than it was before.

But 'the number of trials in my career' is moot
in the first place,

That is arguable. As a precise number you're probably right. But in
broad brushstrokes you can decide, e.g. never to try something, to try
something once and then never again, to try something a dozen times in
your lifetime, to do something once a month, once a week, once a day, or
multiple times a day. Each of these choices entails a monotonically
increasing risk of encountering certain kinds of disasters over your
lifetime.

My personal risk tolerance works out something like this:

Things I'm not willing to try even once: heroin, motorcycle racing
Things I'm willing to try once in my lifetime and never again: going
into space (assuming I ever have the opportunity)
Things I'll do a dozen times: aerobatics
Once a month (on average): skiing
Once a week: Flying GA aircraft
Once a day: getting out of bed in the morning :-)
Multiple times a day: driving on the freeway, eating sushi :-)

rg