Night flying in the mountians in a cessna 150,

1. The probability of experiencing an engine failure (or any other
improbable event for that matter) AT SOME POINT IN YOUR FLYING CAREER
goes up the more you fly. It goes up monotonically but nonlinearly
according to the formula 1-(1-P)^N, which asymptotically approaches 1 as
N gets large.

I have a feeling everyone in this discussion is talking past each other.
However, I'll still pick a nit (since after all, this is usenet).
Probability deals =only= with events whose outcome is not known or not
taken into account. If I take any random 10,000 hours, the probability
of some occurance (like an engine failure) is the same. Let's say the
probability over 10,000 hours is 70%. If I have =already= flown 9,999
hours without a failure, it is =not= true that my chance of failure on
the last hour is 70%. Likewise, if I have already flown those 9,999
hours and already had three engine failures, the chance of having
another in that last hour is =not= zero nor is it negative ("to make up
for the extra failures"). It is the same as the probability of a
failure on the =first= hour.

HOWEVER... the chance that, OVER THOSE 9,999 HOURS flown =plus= the one
not flown, I would =either have an engine failure shortly, =or= look
over my logbook and find that I already had one, would be the original
70%. The key here is including those flown hours without regard to
whether or not there was a failure there - iow as if we did not know the
result.

If you eliminate the hours flown because their outcome is known, then
you can only (correctly) apply probability to the unflown hours.

This is (of course) a different question from the one that says "Here's
my logbook. It has 10,000 one-hour flights in it. I had one engine
failure." and then, as one thumbs through the book saying "not this
one... not this one..." the chance of coming across a flight with an
engine failure =does= increase - because in this case an engine failure
is =guaranteed=. (it already happened).

Running out of fuel is not my idea of "engine failure".

If the fuel pump breaks and thus all four engines quit, did you have an
engine failure?

Jose
r.a.owning and r.a.student trimmed. I don't follow them.
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