In article ,
wrote:

On Fri, 25 Feb 2005 17:16:35 -0800, Ron Garret
wrote:

That's true, but the longer you fly (or play the lottery) the closer
your probability of experiencing an engine failure (or a lottery win)
some time your career approaches 1.

Of course, you might have to fly/play for a *very* long time before that
probability actually gets close to 1, but sooner or later it will be 1
to any desired degree of accuracy. So the statement "fly long enough and
you will experience an engine failure" is pretty close to being true.
The question is how long is "long enough."

rg


This just ain't so.

Yes it is, you just didn't read what I wrote very carefully. Pay
particular attention to the phrase "some time in your career."

Every time you play the lottery, it's like the first time you ever
played it.

Yes, that's true.

It doesn't matter whether you won a jillion yesterday, or haven't won
in 50 years, or never played. The odds are exactly the same.

That depends on what you mean by "the odds". The odds on any one play
are the same, but the cumulative odds of experiencing a win or an engine
failure *at some point in your life* goes up with every play/flight.
Specifically, if the odds of winning on a single try are P then the odds
of winning some time in your career are 1-(1-P)^N where N is the number
of times you play. As long as P is strictly greater than 0 this number
approaches 1 as N grows large. In fact, it is an elementary algebraic
exercise to solve for N given P and the desired cumulative probability
P1.

The behavior of this formula is somewhat counterintuitive. For example,
if P is 0.01 (1 chance in 100 of winning/engine failure on any
particular try) then to have a 99% chance of winning you have to
play/fly about 460 times. To have a 50% chance you only need about 70
tries.

A special case of this formula is when P is very small and N is not too
huge (N1/P). Then (1-P)^N is approximately 1-NP, and the cumulative
probability is approximately 1-(1-NP)=NP. In other words, if the
probability of winning is small then the probability of winning in N
plays is very nearly N times greater than the probability of winning in
1 play. This is a pretty good approximation until the cumulative
probability gets around 10-20% (at which point N is off by 5-10%), which
is to say, it's a pretty close approximation in realistic scenarios for
both lotteries and engine failures.

rg