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Re: What to do IF we regain control of AO-40

> Date: Tue, 19 Dec 2000 02:16:43 -0600
> From: "John P. Toscano" <tosca005@tc.umn.edu>
> Subject: Re: [amsat-bb] What to do IF we regain control of AO-40
> 	[...]
> > Not encouraging.  Logic would then suggest that it has a 50/50 chance
> > of working the next time.  But since it failed on the ground then
> > worked after repair and then failed again we might assume that it may
> > have a 66 percent failure rate?
> 	[...]
> More to the point, the number of observations is too small to make a
> strong statistical prediction of future probabilities.
> Take a penny.  It has a heads and a tails side.  The probability of a
> fair toss coming up heads or tails is infinitesmally different than
> 50% : 50%.  However, if you only toss it 3 times, there is a 12.5%
> probability of getting 3 heads.  It would look like the penny ALWAYS
> comes up heads, but that's only due to lack of data.  (There is ALSO
> a 12.5% chance of getting 3 tails.  The same disclaimer applies.) In
> fact, the most likely result is 2 heads/1 tail (37.5%) or 1 heads/2
> tails (also 37.5%).  There is a zero percent chance of getting the
> right answer (50%/50%) from such a small number of observations.
> 	[...]

If I might quibble with your math, penny tosses are independent events.
That is, the outcome of one experiment does not affect the outcome
of future events.  The probabilities you describe are for independent

However, successive operations of a valve are not independent events.
If a valve sticks once, it is more likely to stick the next time it is
operated.  The events are not independent -- there may be some physical
reason the valve is sticking.  (You probably want to use Bayesian
statistics, or conditional probabilities.  Something of the form:
probability of some event given that some other other event has already

I just thought you would want to know (or not...)

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